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functions_index.qmd
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---
pagetitle: Alphabetical Index
---
<!-- This file is generated by gen_index.py. Do not edit it directly. -->
# Alphabetical Index
## A
<a id='abs' href='#abs' class='anchored unlink'>**abs**:</a>
- <div class='index-container'>[`(complex z) : real`](complex-valued_basic_functions.qmd#index-entry-00d0fd704b516cbdb1c9d8cfdceb177a76481cc4) <span class='detail'>(complex-valued_basic_functions.html)</span></div>
- <div class='index-container'>[`(T x) : T`](integer-valued_basic_functions.qmd#index-entry-c197d7c04ea9bf23cf252f2092111b3c5aadd02d) <span class='detail'>(integer-valued_basic_functions.html)</span></div>
- <div class='index-container'>[`(T x) : T`](real-valued_basic_functions.qmd#index-entry-c197d7c04ea9bf23cf252f2092111b3c5aadd02d) <span class='detail'>(real-valued_basic_functions.html)</span></div>
<a id='acos' href='#acos' class='anchored unlink'>**acos**:</a>
- <div class='index-container'>[`(complex z) : complex`](complex-valued_basic_functions.qmd#index-entry-a3994349ad6faefbd24c6ab7f4c46819b77b7593) <span class='detail'>(complex-valued_basic_functions.html)</span></div>
- <div class='index-container'>[`(T x) : R`](real-valued_basic_functions.qmd#index-entry-c928df245747cbd0d0fdb91212e73e8c3d5ace77) <span class='detail'>(real-valued_basic_functions.html)</span></div>
<a id='acosh' href='#acosh' class='anchored unlink'>**acosh**:</a>
- <div class='index-container'>[`(complex z) : complex`](complex-valued_basic_functions.qmd#index-entry-5d36ca029281c0668f4125ee4d7400c52fcff71c) <span class='detail'>(complex-valued_basic_functions.html)</span></div>
- <div class='index-container'>[`(T x) : R`](real-valued_basic_functions.qmd#index-entry-228328eeafc82944f3bdf9162ddbad97efddff0c) <span class='detail'>(real-valued_basic_functions.html)</span></div>
<a id='add_diag' href='#add_diag' class='anchored unlink'>**add_diag**:</a>
- <div class='index-container'>[`(complex_matrix m, complex_real d) : complex_matrix`](complex_matrix_operations.qmd#index-entry-1bd31f2687a12296c53d88aedd4fe7b91be42e6b) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(complex_matrix m, complex_row_vector d) : complex_matrix`](complex_matrix_operations.qmd#index-entry-ebc82f3647c3357e9ff2d0c3de2f5996ac435a22) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(complex_matrix m, complex_vector d) : complex_matrix`](complex_matrix_operations.qmd#index-entry-c75a27fd3abf5459a2683dc6261be6c0045b71d6) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(matrix m, real d) : matrix`](matrix_operations.qmd#index-entry-6c3894d5b0c4aa6fcae69f294bd4a39e91e3731b) <span class='detail'>(matrix_operations.html)</span></div>
- <div class='index-container'>[`(matrix m, row_vector d) : matrix`](matrix_operations.qmd#index-entry-6c34e1496216d483a0c9876713871db5b36de2b1) <span class='detail'>(matrix_operations.html)</span></div>
- <div class='index-container'>[`(matrix m, vector d) : matrix`](matrix_operations.qmd#index-entry-fd1fe55afe2b42fa662d88b9e836e27f40aed6ed) <span class='detail'>(matrix_operations.html)</span></div>
<a id='algebra_solver' href='#algebra_solver' class='anchored unlink'>**algebra_solver**:</a>
- <div class='index-container'>[`(function algebra_system, vector y_guess, vector theta, data array[] real x_r, array[] int x_i, data real rel_tol, data real f_tol, int max_steps) : vector`](deprecated_functions.qmd#index-entry-717206dad47a7c1194d4b531baf6ffdd3c2d028a) <span class='detail'>(deprecated_functions.html)</span></div>
<a id='algebra_solver_newton' href='#algebra_solver_newton' class='anchored unlink'>**algebra_solver_newton**:</a>
- <div class='index-container'>[`(function algebra_system, vector y_guess, vector theta, data array[] real x_r, array[] int x_i) : vector`](deprecated_functions.qmd#index-entry-c32bcab203b8a5c04135db0647b03444d7effefb) <span class='detail'>(deprecated_functions.html)</span></div>
- <div class='index-container'>[`(function algebra_system, vector y_guess, vector theta, data array[] real x_r, array[] int x_i, data real rel_tol, data real f_tol, int max_steps) : vector`](deprecated_functions.qmd#index-entry-e7af0c43c395b76b7182b00996444a8b8377cac4) <span class='detail'>(deprecated_functions.html)</span></div>
<a id='append_array' href='#append_array' class='anchored unlink'>**append_array**:</a>
- <div class='index-container'>[`(T x, T y) : T`](array_operations.qmd#index-entry-a92d8a1e904382ddb4b800a330feedcb3c04f2c2) <span class='detail'>(array_operations.html)</span></div>
<a id='append_col' href='#append_col' class='anchored unlink'>**append_col**:</a>
- <div class='index-container'>[`(complex x, complex_row_vector y) : complex_row_vector`](complex_matrix_operations.qmd#index-entry-6d9a3c740a41d03e1694a8957fc0686db16578c7) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(complex_matrix x, complex_matrix y) : complex_matrix`](complex_matrix_operations.qmd#index-entry-ffc1159a99f60f1f9ed57275f62abef2a8565af2) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(complex_matrix x, complex_vector y) : complex_matrix`](complex_matrix_operations.qmd#index-entry-3cdea5abd8dcc4f4aa3a63ec4b57e3beb1e548d1) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(complex_row_vector x, complex y) : complex_row_vector`](complex_matrix_operations.qmd#index-entry-435f75dc018a8af24be3ee5ac716757fc6ed0919) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(complex_row_vector x, complex_row_vector y) : complex_row_vector`](complex_matrix_operations.qmd#index-entry-e38bc5278f6ed1cde644188c8eb17161f960454d) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(complex_vector x, complex_matrix y) : complex_matrix`](complex_matrix_operations.qmd#index-entry-925808fc8edc656698d2fa5a95c71e4392b64386) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(complex_vector x, complex_vector y) : complex_matrix`](complex_matrix_operations.qmd#index-entry-a7e682a73b7b4c9c5e762266afcff98336e95763) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(matrix x, matrix y) : matrix`](matrix_operations.qmd#index-entry-9e081ce392909a0df24bb36f03bfa797bed61afc) <span class='detail'>(matrix_operations.html)</span></div>
- <div class='index-container'>[`(matrix x, vector y) : matrix`](matrix_operations.qmd#index-entry-147e13862145f964e1cbb7fcc77a67089a7e5e34) <span class='detail'>(matrix_operations.html)</span></div>
- <div class='index-container'>[`(real x, row_vector y) : row_vector`](matrix_operations.qmd#index-entry-c2a28748bc8f89b100ba5a447e6a37085a0c322f) <span class='detail'>(matrix_operations.html)</span></div>
- <div class='index-container'>[`(row_vector x, real y) : row_vector`](matrix_operations.qmd#index-entry-3bee320543341ea29edfb9d04aca5cc49f8e0b95) <span class='detail'>(matrix_operations.html)</span></div>
- <div class='index-container'>[`(row_vector x, row_vector y) : row_vector`](matrix_operations.qmd#index-entry-21151b3cbeecb129181ef54f899636e705e64a59) <span class='detail'>(matrix_operations.html)</span></div>
- <div class='index-container'>[`(vector x, matrix y) : matrix`](matrix_operations.qmd#index-entry-864b816280933455ecf6e923c13d45129a29b0fd) <span class='detail'>(matrix_operations.html)</span></div>
- <div class='index-container'>[`(vector x, vector y) : matrix`](matrix_operations.qmd#index-entry-58eedcbe1e2b7f299a093b3640fbf33c5ed668a7) <span class='detail'>(matrix_operations.html)</span></div>
<a id='append_row' href='#append_row' class='anchored unlink'>**append_row**:</a>
- <div class='index-container'>[`(complex x, complex_vector y) : complex_vector`](complex_matrix_operations.qmd#index-entry-a9fd96b44e573f1bb61f0cf8266f4bdc7a805dd3) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(complex_matrix x, complex_matrix y) : complex_matrix`](complex_matrix_operations.qmd#index-entry-ca4bcfd187ccd1d2f4f0816dfc7f2b31f95ff4b2) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(complex_matrix x, complex_row_vector y) : complex_matrix`](complex_matrix_operations.qmd#index-entry-a0c350c64c953d5aa3a9de44bc62448e1b90233d) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(complex_row_vector x, complex_matrix y) : complex_matrix`](complex_matrix_operations.qmd#index-entry-cbbd35ff37b9d41a2c66dbb60739e4b40a3b2c92) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(complex_row_vector x, complex_row_vector y) : complex_matrix`](complex_matrix_operations.qmd#index-entry-d3f8a5fb9c0e574f1b8fc41e58b9ff4d768b1316) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(complex_vector x, complex y) : complex_vector`](complex_matrix_operations.qmd#index-entry-8140228bb8f902ae61c5e8eba43e81e6d32de7bd) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(complex_vector x, complex_vector y) : complex_vector`](complex_matrix_operations.qmd#index-entry-101152cf279176e6d126b58acb513a382b3076db) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(matrix x, matrix y) : matrix`](matrix_operations.qmd#index-entry-135048f5cff906d2164940e5b4b34af8be6d9972) <span class='detail'>(matrix_operations.html)</span></div>
- <div class='index-container'>[`(matrix x, row_vector y) : matrix`](matrix_operations.qmd#index-entry-1f14ca719bab4b3d6eff9ae371f10a5fac48b85c) <span class='detail'>(matrix_operations.html)</span></div>
- <div class='index-container'>[`(real x, vector y) : vector`](matrix_operations.qmd#index-entry-be0707e02550507f8665c2fa85d337275029a3c5) <span class='detail'>(matrix_operations.html)</span></div>
- <div class='index-container'>[`(row_vector x, matrix y) : matrix`](matrix_operations.qmd#index-entry-54b2d5adfa559ab3f257ab5acd8f7f57c4fafbf9) <span class='detail'>(matrix_operations.html)</span></div>
- <div class='index-container'>[`(row_vector x, row_vector y) : matrix`](matrix_operations.qmd#index-entry-6f6580337b50792274a5b4740260362421589d97) <span class='detail'>(matrix_operations.html)</span></div>
- <div class='index-container'>[`(vector x, real y) : vector`](matrix_operations.qmd#index-entry-626869953f524fd6120faadc1ed9dcdb8f710167) <span class='detail'>(matrix_operations.html)</span></div>
- <div class='index-container'>[`(vector x, vector y) : vector`](matrix_operations.qmd#index-entry-f406895b07b910f47d6bd89b7d603c711582be11) <span class='detail'>(matrix_operations.html)</span></div>
<a id='arg' href='#arg' class='anchored unlink'>**arg**:</a>
- <div class='index-container'>[`(complex z) : real`](complex-valued_basic_functions.qmd#index-entry-14bed65ae47bba6447a5f2bb816ef9fe09bb8dd2) <span class='detail'>(complex-valued_basic_functions.html)</span></div>
<a id='asin' href='#asin' class='anchored unlink'>**asin**:</a>
- <div class='index-container'>[`(complex z) : complex`](complex-valued_basic_functions.qmd#index-entry-e8dbabd64d9392bddc505ca75aaf4aa1ef314c3d) <span class='detail'>(complex-valued_basic_functions.html)</span></div>
- <div class='index-container'>[`(T x) : R`](real-valued_basic_functions.qmd#index-entry-f2bf9ebf3337e4f590b7f30ebe4aaeb04d2ca9a3) <span class='detail'>(real-valued_basic_functions.html)</span></div>
<a id='asinh' href='#asinh' class='anchored unlink'>**asinh**:</a>
- <div class='index-container'>[`(complex z) : complex`](complex-valued_basic_functions.qmd#index-entry-8fd580d63363a17a791a49b5b536b475a5bef834) <span class='detail'>(complex-valued_basic_functions.html)</span></div>
- <div class='index-container'>[`(T x) : R`](real-valued_basic_functions.qmd#index-entry-a267074b1b9acb770b679aeaca1e79f326fecd09) <span class='detail'>(real-valued_basic_functions.html)</span></div>
<a id='atan' href='#atan' class='anchored unlink'>**atan**:</a>
- <div class='index-container'>[`(complex z) : complex`](complex-valued_basic_functions.qmd#index-entry-f60565512ea3debd990f3ae7ee57978b45210673) <span class='detail'>(complex-valued_basic_functions.html)</span></div>
- <div class='index-container'>[`(T x) : R`](real-valued_basic_functions.qmd#index-entry-4ff6fd29f63ba53b4b854f16fb4122d25f817257) <span class='detail'>(real-valued_basic_functions.html)</span></div>
<a id='atan2' href='#atan2' class='anchored unlink'>**atan2**:</a>
- <div class='index-container'>[`(T y, T x) : R`](real-valued_basic_functions.qmd#index-entry-bf8aeecad9e7aec2135da1c0e68b6c6e380eb65c) <span class='detail'>(real-valued_basic_functions.html)</span></div>
<a id='atanh' href='#atanh' class='anchored unlink'>**atanh**:</a>
- <div class='index-container'>[`(complex z) : complex`](complex-valued_basic_functions.qmd#index-entry-51283fe4d2aef2c21fe4abe006b88ed2a9ab8b92) <span class='detail'>(complex-valued_basic_functions.html)</span></div>
- <div class='index-container'>[`(T x) : R`](real-valued_basic_functions.qmd#index-entry-1a2910acee55dabfad98224fee341fccc8af7cb0) <span class='detail'>(real-valued_basic_functions.html)</span></div>
## B
<a id='bernoulli' href='#bernoulli' class='anchored unlink'>**bernoulli**:</a>
- <div class='index-container'>[distribution statement](binary_distributions.qmd#index-entry-7bb1d0fe6798b5a1780314a5829d10cf070cb584) <span class='detail'>(binary_distributions.html)</span></div>
<a id='bernoulli_cdf' href='#bernoulli_cdf' class='anchored unlink'>**bernoulli_cdf**:</a>
- <div class='index-container'>[`(ints y | reals theta) : real`](binary_distributions.qmd#index-entry-fba3b9784cb145bce67dc4b2b5b7e6beedcde682) <span class='detail'>(binary_distributions.html)</span></div>
<a id='bernoulli_lccdf' href='#bernoulli_lccdf' class='anchored unlink'>**bernoulli_lccdf**:</a>
- <div class='index-container'>[`(ints y | reals theta) : real`](binary_distributions.qmd#index-entry-8669190b9a16302c87a7a759518c13b507ba01d5) <span class='detail'>(binary_distributions.html)</span></div>
<a id='bernoulli_lcdf' href='#bernoulli_lcdf' class='anchored unlink'>**bernoulli_lcdf**:</a>
- <div class='index-container'>[`(ints y | reals theta) : real`](binary_distributions.qmd#index-entry-aee9b81290c031013a18766f7c73a0d661732bc1) <span class='detail'>(binary_distributions.html)</span></div>
<a id='bernoulli_logit' href='#bernoulli_logit' class='anchored unlink'>**bernoulli_logit**:</a>
- <div class='index-container'>[distribution statement](binary_distributions.qmd#index-entry-778ebacd22f9f00e5c91bc26ac55e9ef4530423a) <span class='detail'>(binary_distributions.html)</span></div>
<a id='bernoulli_logit_glm' href='#bernoulli_logit_glm' class='anchored unlink'>**bernoulli_logit_glm**:</a>
- <div class='index-container'>[distribution statement](binary_distributions.qmd#index-entry-cc775222ff8767d0ddb5f23a1f67b77eac3ef7f1) <span class='detail'>(binary_distributions.html)</span></div>
<a id='bernoulli_logit_glm_lpmf' href='#bernoulli_logit_glm_lpmf' class='anchored unlink'>**bernoulli_logit_glm_lpmf**:</a>
- <div class='index-container'>[`(array[] int y | matrix x, real alpha, vector beta) : real`](binary_distributions.qmd#index-entry-3c4e9f4b1e229095991ef7d66e815550e6189de8) <span class='detail'>(binary_distributions.html)</span></div>
- <div class='index-container'>[`(array[] int y | matrix x, vector alpha, vector beta) : real`](binary_distributions.qmd#index-entry-5ba40a905c796c1bcd54602e2cdde64d36486f54) <span class='detail'>(binary_distributions.html)</span></div>
- <div class='index-container'>[`(array[] int y | row_vector x, real alpha, vector beta) : real`](binary_distributions.qmd#index-entry-e6ed6ee376ada4610e458b39eb40199e201a1752) <span class='detail'>(binary_distributions.html)</span></div>
- <div class='index-container'>[`(array[] int y | row_vector x, vector alpha, vector beta) : real`](binary_distributions.qmd#index-entry-616a93c521e26ed8b747183681c8f77775ffad47) <span class='detail'>(binary_distributions.html)</span></div>
- <div class='index-container'>[`(int y | matrix x, real alpha, vector beta) : real`](binary_distributions.qmd#index-entry-b84bfdcb0924789b419a611e996c6185d4c9ec71) <span class='detail'>(binary_distributions.html)</span></div>
- <div class='index-container'>[`(int y | matrix x, vector alpha, vector beta) : real`](binary_distributions.qmd#index-entry-8595b1aadcd41c4266263ddfa5529f3381f42c02) <span class='detail'>(binary_distributions.html)</span></div>
<a id='bernoulli_logit_glm_lupmf' href='#bernoulli_logit_glm_lupmf' class='anchored unlink'>**bernoulli_logit_glm_lupmf**:</a>
- <div class='index-container'>[`(array[] int y | matrix x, real alpha, vector beta) : real`](binary_distributions.qmd#index-entry-171d0ba3be3d570d3167c621b3a6e7bac0f34b49) <span class='detail'>(binary_distributions.html)</span></div>
- <div class='index-container'>[`(array[] int y | matrix x, vector alpha, vector beta) : real`](binary_distributions.qmd#index-entry-75e3b277f495a675db21144dfd54403c5b61e4b1) <span class='detail'>(binary_distributions.html)</span></div>
- <div class='index-container'>[`(array[] int y | row_vector x, real alpha, vector beta) : real`](binary_distributions.qmd#index-entry-75fe439a6c3fdf76668cd7afcb6fcc6d7d2aee4e) <span class='detail'>(binary_distributions.html)</span></div>
- <div class='index-container'>[`(array[] int y | row_vector x, vector alpha, vector beta) : real`](binary_distributions.qmd#index-entry-06917600c21e8a8c04a19d2e00412d5adc619330) <span class='detail'>(binary_distributions.html)</span></div>
- <div class='index-container'>[`(int y | matrix x, real alpha, vector beta) : real`](binary_distributions.qmd#index-entry-58e5cd13a2585a62b0a4305dfb70b2276419bd31) <span class='detail'>(binary_distributions.html)</span></div>
- <div class='index-container'>[`(int y | matrix x, vector alpha, vector beta) : real`](binary_distributions.qmd#index-entry-09934df75edb200a53b9e3f261e389a5c908bb0e) <span class='detail'>(binary_distributions.html)</span></div>
<a id='bernoulli_logit_glm_rng' href='#bernoulli_logit_glm_rng' class='anchored unlink'>**bernoulli_logit_glm_rng**:</a>
- <div class='index-container'>[`(matrix x, vector alpha, vector beta) : array[] int`](binary_distributions.qmd#index-entry-1caea52d2e1f6a4419889e2a233b20178f262a89) <span class='detail'>(binary_distributions.html)</span></div>
- <div class='index-container'>[`(row_vector x, vector alpha, vector beta) : array[] int`](binary_distributions.qmd#index-entry-486921f4f12ed8fec65ef02c934ac90a947400a0) <span class='detail'>(binary_distributions.html)</span></div>
<a id='bernoulli_logit_lpmf' href='#bernoulli_logit_lpmf' class='anchored unlink'>**bernoulli_logit_lpmf**:</a>
- <div class='index-container'>[`(ints y | reals alpha) : real`](binary_distributions.qmd#index-entry-cad8c604c21adb32fa4d2b5789b7a3888ebaf554) <span class='detail'>(binary_distributions.html)</span></div>
<a id='bernoulli_logit_lupmf' href='#bernoulli_logit_lupmf' class='anchored unlink'>**bernoulli_logit_lupmf**:</a>
- <div class='index-container'>[`(ints y | reals alpha) : real`](binary_distributions.qmd#index-entry-74fd84a52ce20d7b2b2914acecea456438e780a5) <span class='detail'>(binary_distributions.html)</span></div>
<a id='bernoulli_logit_rng' href='#bernoulli_logit_rng' class='anchored unlink'>**bernoulli_logit_rng**:</a>
- <div class='index-container'>[`(reals alpha) : R`](binary_distributions.qmd#index-entry-275ab72ec22b30d37f9bc02991be25a6bd23f49a) <span class='detail'>(binary_distributions.html)</span></div>
<a id='bernoulli_lpmf' href='#bernoulli_lpmf' class='anchored unlink'>**bernoulli_lpmf**:</a>
- <div class='index-container'>[`(ints y | reals theta) : real`](binary_distributions.qmd#index-entry-d5704b5b3fb92b6acbe402518995306b417633a6) <span class='detail'>(binary_distributions.html)</span></div>
<a id='bernoulli_lupmf' href='#bernoulli_lupmf' class='anchored unlink'>**bernoulli_lupmf**:</a>
- <div class='index-container'>[`(ints y | reals theta) : real`](binary_distributions.qmd#index-entry-d71dcd384cd23a024264d9e21555dafc50336c88) <span class='detail'>(binary_distributions.html)</span></div>
<a id='bernoulli_rng' href='#bernoulli_rng' class='anchored unlink'>**bernoulli_rng**:</a>
- <div class='index-container'>[`(reals theta) : R`](binary_distributions.qmd#index-entry-8e32579888cc9b06d6c81f2c372fc7b94641ce47) <span class='detail'>(binary_distributions.html)</span></div>
<a id='bessel_first_kind' href='#bessel_first_kind' class='anchored unlink'>**bessel_first_kind**:</a>
- <div class='index-container'>[`(int v, real x) : real`](real-valued_basic_functions.qmd#index-entry-3bc21536b0609c1753010054298a02498c21c610) <span class='detail'>(real-valued_basic_functions.html)</span></div>
- <div class='index-container'>[`(T1 x, T2 y) : R`](real-valued_basic_functions.qmd#index-entry-88cb374bd5bc83af305e30102a59f6e38cd04165) <span class='detail'>(real-valued_basic_functions.html)</span></div>
<a id='bessel_second_kind' href='#bessel_second_kind' class='anchored unlink'>**bessel_second_kind**:</a>
- <div class='index-container'>[`(int v, real x) : real`](real-valued_basic_functions.qmd#index-entry-a76f46f2143eed84250e51f4f9fa21abf7ff8085) <span class='detail'>(real-valued_basic_functions.html)</span></div>
- <div class='index-container'>[`(T1 x, T2 y) : R`](real-valued_basic_functions.qmd#index-entry-7d09ab04cf9e5ad369f0475cf89c0dcf0e6cf137) <span class='detail'>(real-valued_basic_functions.html)</span></div>
<a id='beta' href='#beta' class='anchored unlink'>**beta**:</a>
- <div class='index-container'>[`(real alpha, real beta) : real`](real-valued_basic_functions.qmd#index-entry-bbec535fbcce7c57b2dd2cc189383f0c180038ed) <span class='detail'>(real-valued_basic_functions.html)</span></div>
- <div class='index-container'>[`(T1 x, T2 y) : R`](real-valued_basic_functions.qmd#index-entry-faea3c6dc569671c76ab57211c00ebac2394742c) <span class='detail'>(real-valued_basic_functions.html)</span></div>
- <div class='index-container'>[distribution statement](continuous_distributions_on_0_1.qmd#index-entry-ed6b0e2a1365933147e892aab802b3da10b2bb6d) <span class='detail'>(continuous_distributions_on_0_1.html)</span></div>
<a id='beta_binomial' href='#beta_binomial' class='anchored unlink'>**beta_binomial**:</a>
- <div class='index-container'>[distribution statement](bounded_discrete_distributions.qmd#index-entry-989d2a39dee7b5799bfbc8bc1274f0307b4894a2) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='beta_binomial_cdf' href='#beta_binomial_cdf' class='anchored unlink'>**beta_binomial_cdf**:</a>
- <div class='index-container'>[`(ints n | ints N, reals alpha, reals beta) : real`](bounded_discrete_distributions.qmd#index-entry-ba9143f242e640009de45aa086f5082832c63ac0) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='beta_binomial_lccdf' href='#beta_binomial_lccdf' class='anchored unlink'>**beta_binomial_lccdf**:</a>
- <div class='index-container'>[`(ints n | ints N, reals alpha, reals beta) : real`](bounded_discrete_distributions.qmd#index-entry-865ef09530f64c02214e607ccdee381fca79831c) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='beta_binomial_lcdf' href='#beta_binomial_lcdf' class='anchored unlink'>**beta_binomial_lcdf**:</a>
- <div class='index-container'>[`(ints n | ints N, reals alpha, reals beta) : real`](bounded_discrete_distributions.qmd#index-entry-85c6b546de98c04c4454a1521ecc3fad803b7994) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='beta_binomial_lpmf' href='#beta_binomial_lpmf' class='anchored unlink'>**beta_binomial_lpmf**:</a>
- <div class='index-container'>[`(ints n | ints N, reals alpha, reals beta) : real`](bounded_discrete_distributions.qmd#index-entry-5e63ca67ce5a7886091457e81ed9ad8abad1af53) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='beta_binomial_lupmf' href='#beta_binomial_lupmf' class='anchored unlink'>**beta_binomial_lupmf**:</a>
- <div class='index-container'>[`(ints n | ints N, reals alpha, reals beta) : real`](bounded_discrete_distributions.qmd#index-entry-91a92506bc4098570edad18162c4925e53b060cb) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='beta_binomial_rng' href='#beta_binomial_rng' class='anchored unlink'>**beta_binomial_rng**:</a>
- <div class='index-container'>[`(ints N, reals alpha, reals beta) : R`](bounded_discrete_distributions.qmd#index-entry-2103ccd2a4395de2cf0bc035105ff78f46f83671) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='beta_cdf' href='#beta_cdf' class='anchored unlink'>**beta_cdf**:</a>
- <div class='index-container'>[`(reals theta | reals alpha, reals beta) : real`](continuous_distributions_on_0_1.qmd#index-entry-096320ad72e962315021c5f04c98350b8ff52744) <span class='detail'>(continuous_distributions_on_0_1.html)</span></div>
<a id='beta_lccdf' href='#beta_lccdf' class='anchored unlink'>**beta_lccdf**:</a>
- <div class='index-container'>[`(reals theta | reals alpha, reals beta) : real`](continuous_distributions_on_0_1.qmd#index-entry-70ce7e460a07bc188c0e0eb7ab6c0ed1d212d523) <span class='detail'>(continuous_distributions_on_0_1.html)</span></div>
<a id='beta_lcdf' href='#beta_lcdf' class='anchored unlink'>**beta_lcdf**:</a>
- <div class='index-container'>[`(reals theta | reals alpha, reals beta) : real`](continuous_distributions_on_0_1.qmd#index-entry-a3067ae5b48a826e8ad6971507a45b59a9e242ed) <span class='detail'>(continuous_distributions_on_0_1.html)</span></div>
<a id='beta_lpdf' href='#beta_lpdf' class='anchored unlink'>**beta_lpdf**:</a>
- <div class='index-container'>[`(reals theta | reals alpha, reals beta) : real`](continuous_distributions_on_0_1.qmd#index-entry-93d2282b7bada6cf97c5977413fb03d509c396ea) <span class='detail'>(continuous_distributions_on_0_1.html)</span></div>
<a id='beta_lupdf' href='#beta_lupdf' class='anchored unlink'>**beta_lupdf**:</a>
- <div class='index-container'>[`(reals theta | reals alpha, reals beta) : real`](continuous_distributions_on_0_1.qmd#index-entry-340181b236cc79820c87cfca7dc7e8d9ef5bdf6e) <span class='detail'>(continuous_distributions_on_0_1.html)</span></div>
<a id='beta_neg_binomial' href='#beta_neg_binomial' class='anchored unlink'>**beta_neg_binomial**:</a>
- <div class='index-container'>[distribution statement](unbounded_discrete_distributions.qmd#index-entry-0c7465aa1beceb6e7e303af36b60e2b847fc562a) <span class='detail'>(unbounded_discrete_distributions.html)</span></div>
<a id='beta_neg_binomial_cdf' href='#beta_neg_binomial_cdf' class='anchored unlink'>**beta_neg_binomial_cdf**:</a>
- <div class='index-container'>[`(ints n | reals r, reals alpha, reals beta) : real`](unbounded_discrete_distributions.qmd#index-entry-ecce69045f7901c0a69ccc67aaae5ddda48304b2) <span class='detail'>(unbounded_discrete_distributions.html)</span></div>
<a id='beta_neg_binomial_lccdf' href='#beta_neg_binomial_lccdf' class='anchored unlink'>**beta_neg_binomial_lccdf**:</a>
- <div class='index-container'>[`(ints n | reals r, reals alpha, reals beta) : real`](unbounded_discrete_distributions.qmd#index-entry-50c63a123857b7480722a4aeb3d884c95317cdc3) <span class='detail'>(unbounded_discrete_distributions.html)</span></div>
<a id='beta_neg_binomial_lcdf' href='#beta_neg_binomial_lcdf' class='anchored unlink'>**beta_neg_binomial_lcdf**:</a>
- <div class='index-container'>[`(ints n | reals r, reals alpha, reals beta) : real`](unbounded_discrete_distributions.qmd#index-entry-fbab2aa3f292996672306979423648761d0ab98f) <span class='detail'>(unbounded_discrete_distributions.html)</span></div>
<a id='beta_neg_binomial_lpmf' href='#beta_neg_binomial_lpmf' class='anchored unlink'>**beta_neg_binomial_lpmf**:</a>
- <div class='index-container'>[`(ints n | reals r, reals alpha, reals beta) : real`](unbounded_discrete_distributions.qmd#index-entry-9d835cd7ed67218478d70e1db49912bf2d710a1e) <span class='detail'>(unbounded_discrete_distributions.html)</span></div>
<a id='beta_neg_binomial_lupmf' href='#beta_neg_binomial_lupmf' class='anchored unlink'>**beta_neg_binomial_lupmf**:</a>
- <div class='index-container'>[`(ints n | reals r, reals alpha, reals beta) : real`](unbounded_discrete_distributions.qmd#index-entry-1bd0b7fec4d1f3e315d4328c1844d15641058615) <span class='detail'>(unbounded_discrete_distributions.html)</span></div>
<a id='beta_neg_binomial_rng' href='#beta_neg_binomial_rng' class='anchored unlink'>**beta_neg_binomial_rng**:</a>
- <div class='index-container'>[`(reals r, reals alpha, reals beta) : R`](unbounded_discrete_distributions.qmd#index-entry-8c97955cf7e95ec459f434cad32f31a963d196cd) <span class='detail'>(unbounded_discrete_distributions.html)</span></div>
<a id='beta_proportion' href='#beta_proportion' class='anchored unlink'>**beta_proportion**:</a>
- <div class='index-container'>[distribution statement](continuous_distributions_on_0_1.qmd#index-entry-9e3ba228a8bb07d871e13efa26340614b125cd7f) <span class='detail'>(continuous_distributions_on_0_1.html)</span></div>
<a id='beta_proportion_lccdf' href='#beta_proportion_lccdf' class='anchored unlink'>**beta_proportion_lccdf**:</a>
- <div class='index-container'>[`(reals theta | reals mu, reals kappa) : real`](continuous_distributions_on_0_1.qmd#index-entry-8c5423cb82f066b9e55e6fdeefcbb2355698308f) <span class='detail'>(continuous_distributions_on_0_1.html)</span></div>
<a id='beta_proportion_lcdf' href='#beta_proportion_lcdf' class='anchored unlink'>**beta_proportion_lcdf**:</a>
- <div class='index-container'>[`(reals theta | reals mu, reals kappa) : real`](continuous_distributions_on_0_1.qmd#index-entry-61a129c59e7facb5ab538ca66fb2f4f1750bf7e1) <span class='detail'>(continuous_distributions_on_0_1.html)</span></div>
<a id='beta_proportion_lpdf' href='#beta_proportion_lpdf' class='anchored unlink'>**beta_proportion_lpdf**:</a>
- <div class='index-container'>[distribution statement](continuous_distributions_on_0_1.qmd#index-entry-17df822665a57e3384bab6b0afda777c4143c7e0) <span class='detail'>(continuous_distributions_on_0_1.html)</span></div>
<a id='beta_proportion_lupdf' href='#beta_proportion_lupdf' class='anchored unlink'>**beta_proportion_lupdf**:</a>
- <div class='index-container'>[distribution statement](continuous_distributions_on_0_1.qmd#index-entry-2405cab8a4a9d35c52fc1b0951a25d3074339f72) <span class='detail'>(continuous_distributions_on_0_1.html)</span></div>
<a id='beta_proportion_rng' href='#beta_proportion_rng' class='anchored unlink'>**beta_proportion_rng**:</a>
- <div class='index-container'>[`(reals mu, reals kappa) : R`](continuous_distributions_on_0_1.qmd#index-entry-55d15275007130c8e57a41bf24370311b3581959) <span class='detail'>(continuous_distributions_on_0_1.html)</span></div>
<a id='beta_rng' href='#beta_rng' class='anchored unlink'>**beta_rng**:</a>
- <div class='index-container'>[`(reals alpha, reals beta) : R`](continuous_distributions_on_0_1.qmd#index-entry-447854f88734efbef65bc89140a035fe0f16cc74) <span class='detail'>(continuous_distributions_on_0_1.html)</span></div>
<a id='binary_log_loss' href='#binary_log_loss' class='anchored unlink'>**binary_log_loss**:</a>
- <div class='index-container'>[`(int y, real y_hat) : real`](real-valued_basic_functions.qmd#index-entry-44fff3495ce5cd36ebde4587e802cb7bdc795794) <span class='detail'>(real-valued_basic_functions.html)</span></div>
- <div class='index-container'>[`(T1 x, T2 y) : R`](real-valued_basic_functions.qmd#index-entry-05d751372242ac11c1c7356d09fb0341276b897c) <span class='detail'>(real-valued_basic_functions.html)</span></div>
<a id='binomial' href='#binomial' class='anchored unlink'>**binomial**:</a>
- <div class='index-container'>[distribution statement](bounded_discrete_distributions.qmd#index-entry-04d7179640d2a656dc12c9b1c5ed98a04620ef81) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='binomial_cdf' href='#binomial_cdf' class='anchored unlink'>**binomial_cdf**:</a>
- <div class='index-container'>[`(ints n | ints N, reals theta) : real`](bounded_discrete_distributions.qmd#index-entry-304f7e96d0cb2c64c6ff84e3b67d56b0ff58e1cc) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='binomial_lccdf' href='#binomial_lccdf' class='anchored unlink'>**binomial_lccdf**:</a>
- <div class='index-container'>[`(ints n | ints N, reals theta) : real`](bounded_discrete_distributions.qmd#index-entry-51c3d20caad1f513ce40fc1c8af17ec9c1d82eca) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='binomial_lcdf' href='#binomial_lcdf' class='anchored unlink'>**binomial_lcdf**:</a>
- <div class='index-container'>[`(ints n | ints N, reals theta) : real`](bounded_discrete_distributions.qmd#index-entry-0414522d06188bdb5122e227051e36f457a2a1c6) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='binomial_logit' href='#binomial_logit' class='anchored unlink'>**binomial_logit**:</a>
- <div class='index-container'>[distribution statement](bounded_discrete_distributions.qmd#index-entry-0c90bd9f55ca58f075077bde8a8c7fa4b260b346) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='binomial_logit_glm' href='#binomial_logit_glm' class='anchored unlink'>**binomial_logit_glm**:</a>
- <div class='index-container'>[distribution statement](bounded_discrete_distributions.qmd#index-entry-c8c31102f7b5abf104dd462dd52e20ad4ee53d24) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='binomial_logit_glm_lpmf' href='#binomial_logit_glm_lpmf' class='anchored unlink'>**binomial_logit_glm_lpmf**:</a>
- <div class='index-container'>[`(array[] int n | array[] int N, matrix x, real alpha, vector beta) : real`](bounded_discrete_distributions.qmd#index-entry-3f85893b1fea02de309015929662b0b20beb9309) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
- <div class='index-container'>[`(array[] int n | array[] int N, matrix x, vector alpha, vector beta) : real`](bounded_discrete_distributions.qmd#index-entry-1882ad2cd7ca87f3d1050d5be18f2adcc431d794) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
- <div class='index-container'>[`(array[] int n | array[] int N, row_vector x, real alpha, vector beta) : real`](bounded_discrete_distributions.qmd#index-entry-e1b1936f95d710de4ad0682cbf085a530908d39a) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
- <div class='index-container'>[`(array[] int n | array[] int N, row_vector x, vector alpha, vector beta) : real`](bounded_discrete_distributions.qmd#index-entry-e38992f8d67e6ef5ce4e08abdfb07fe5ff1d3c9a) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
- <div class='index-container'>[`(int n | int N, matrix x, real alpha, vector beta) : real`](bounded_discrete_distributions.qmd#index-entry-3da9351d4d4f1762941c69259fcfddf39dd65eae) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
- <div class='index-container'>[`(int n | int N, matrix x, vector alpha, vector beta) : real`](bounded_discrete_distributions.qmd#index-entry-a7a84a22f1a74964827e7e3c3c2ecb0233e5cf37) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='binomial_logit_glm_lupmf' href='#binomial_logit_glm_lupmf' class='anchored unlink'>**binomial_logit_glm_lupmf**:</a>
- <div class='index-container'>[`(array[] int n | array[] int N, matrix x, real alpha, vector beta) : real`](bounded_discrete_distributions.qmd#index-entry-f45f2f92b4005c55ad8f5cdd2285c9708fefe806) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
- <div class='index-container'>[`(array[] int n | array[] int N, matrix x, vector alpha, vector beta) : real`](bounded_discrete_distributions.qmd#index-entry-9889fa94aac823796e6949b79108363bfbbbaa9d) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
- <div class='index-container'>[`(array[] int n | array[] int N, row_vector x, real alpha, vector beta) : real`](bounded_discrete_distributions.qmd#index-entry-428627db76fccf914ceaefa4cd5884bd131556b9) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
- <div class='index-container'>[`(array[] int n | array[] int N, row_vector x, vector alpha, vector beta) : real`](bounded_discrete_distributions.qmd#index-entry-7d6e3169c60256f12c03411a7509e0370a1ee157) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
- <div class='index-container'>[`(int n | int N, matrix x, real alpha, vector beta) : real`](bounded_discrete_distributions.qmd#index-entry-de178183d4185e13aa59ffee44cc49a8ba2dc7e9) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
- <div class='index-container'>[`(int n | int N, matrix x, vector alpha, vector beta) : real`](bounded_discrete_distributions.qmd#index-entry-588f750b18cf5987a93c0022ecc43c232efc3e24) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='binomial_logit_lpmf' href='#binomial_logit_lpmf' class='anchored unlink'>**binomial_logit_lpmf**:</a>
- <div class='index-container'>[`(ints n | ints N, reals alpha) : real`](bounded_discrete_distributions.qmd#index-entry-2231c87f532ddd0458a862cf4cc6e80ca618fc99) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='binomial_logit_lupmf' href='#binomial_logit_lupmf' class='anchored unlink'>**binomial_logit_lupmf**:</a>
- <div class='index-container'>[`(ints n | ints N, reals alpha) : real`](bounded_discrete_distributions.qmd#index-entry-2fe1708373b5f137c68a8ac756400a2be58856fd) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='binomial_lpmf' href='#binomial_lpmf' class='anchored unlink'>**binomial_lpmf**:</a>
- <div class='index-container'>[`(ints n | ints N, reals theta) : real`](bounded_discrete_distributions.qmd#index-entry-8798e65d04763014c36aa7b9c6509c71c538efb6) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='binomial_lupmf' href='#binomial_lupmf' class='anchored unlink'>**binomial_lupmf**:</a>
- <div class='index-container'>[`(ints n | ints N, reals theta) : real`](bounded_discrete_distributions.qmd#index-entry-d9a18d8e413d00481fdf0a47e523a5232870fc25) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='binomial_rng' href='#binomial_rng' class='anchored unlink'>**binomial_rng**:</a>
- <div class='index-container'>[`(ints N, reals theta) : R`](bounded_discrete_distributions.qmd#index-entry-15ce73a3a3caa43cbbe65c4e58495cf18ed8886e) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='block' href='#block' class='anchored unlink'>**block**:</a>
- <div class='index-container'>[`(complex_matrix x, int i, int j, int n_rows, int n_cols) : complex_matrix`](complex_matrix_operations.qmd#index-entry-2d1266e93b2287bbb26f4015769ebc779ef29f81) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(matrix x, int i, int j, int n_rows, int n_cols) : matrix`](matrix_operations.qmd#index-entry-ed12d70d85024ac1bb87c1c1c5971659fb5f2cc1) <span class='detail'>(matrix_operations.html)</span></div>
## C
<a id='categorical' href='#categorical' class='anchored unlink'>**categorical**:</a>
- <div class='index-container'>[distribution statement](bounded_discrete_distributions.qmd#index-entry-bd19bcb6308a78b3569b39d80a5050df0380eae5) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='categorical_logit' href='#categorical_logit' class='anchored unlink'>**categorical_logit**:</a>
- <div class='index-container'>[distribution statement](bounded_discrete_distributions.qmd#index-entry-2ffcb74c4ba70a5424f59a10d068421051f4963c) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='categorical_logit_glm' href='#categorical_logit_glm' class='anchored unlink'>**categorical_logit_glm**:</a>
- <div class='index-container'>[distribution statement](bounded_discrete_distributions.qmd#index-entry-9d4042f47493597a30307ede3c9743ad09549f4d) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='categorical_logit_glm_lpmf' href='#categorical_logit_glm_lpmf' class='anchored unlink'>**categorical_logit_glm_lpmf**:</a>
- <div class='index-container'>[`(array[] int y | matrix x, vector alpha, matrix beta) : real`](bounded_discrete_distributions.qmd#index-entry-512bbe1dc00cc3ef23d8272ec1c0da56105f1c42) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
- <div class='index-container'>[`(array[] int y | row_vector x, vector alpha, matrix beta) : real`](bounded_discrete_distributions.qmd#index-entry-8f756acaa498908962c53d1a6b0af17598fd8524) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
- <div class='index-container'>[`(int y | matrix x, vector alpha, matrix beta) : real`](bounded_discrete_distributions.qmd#index-entry-b41f55e8856f7805a26e7a2ee183d028df87f769) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
- <div class='index-container'>[`(int y | row_vector x, vector alpha, matrix beta) : real`](bounded_discrete_distributions.qmd#index-entry-4e1f97ef06a17d796b0a7cc5ae22003b03f95401) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='categorical_logit_glm_lupmf' href='#categorical_logit_glm_lupmf' class='anchored unlink'>**categorical_logit_glm_lupmf**:</a>
- <div class='index-container'>[`(array[] int y | matrix x, vector alpha, matrix beta) : real`](bounded_discrete_distributions.qmd#index-entry-09da9504e8676f6b35327c85d13771d63f77b83b) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
- <div class='index-container'>[`(array[] int y | row_vector x, vector alpha, matrix beta) : real`](bounded_discrete_distributions.qmd#index-entry-518462f77e8ba90187fbc7302cb54236a0c8b333) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
- <div class='index-container'>[`(int y | matrix x, vector alpha, matrix beta) : real`](bounded_discrete_distributions.qmd#index-entry-866be3d0f99507bddabbbe0652cce251858d2c37) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
- <div class='index-container'>[`(int y | row_vector x, vector alpha, matrix beta) : real`](bounded_discrete_distributions.qmd#index-entry-3e5402103e17dd48bb2625e6a2b76c48782a1a72) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='categorical_logit_lpmf' href='#categorical_logit_lpmf' class='anchored unlink'>**categorical_logit_lpmf**:</a>
- <div class='index-container'>[`(ints y | vector beta) : real`](bounded_discrete_distributions.qmd#index-entry-da54bfd2ecc17ee462038470f94a63c7be030e08) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='categorical_logit_lupmf' href='#categorical_logit_lupmf' class='anchored unlink'>**categorical_logit_lupmf**:</a>
- <div class='index-container'>[`(ints y | vector beta) : real`](bounded_discrete_distributions.qmd#index-entry-07422d7054ee8fa6c1816736064c38c694563486) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='categorical_logit_rng' href='#categorical_logit_rng' class='anchored unlink'>**categorical_logit_rng**:</a>
- <div class='index-container'>[`(vector beta) : int`](bounded_discrete_distributions.qmd#index-entry-2da030b7d2ce945503ab8ef37e97ee5afc78305e) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='categorical_lpmf' href='#categorical_lpmf' class='anchored unlink'>**categorical_lpmf**:</a>
- <div class='index-container'>[`(ints y | vector theta) : real`](bounded_discrete_distributions.qmd#index-entry-9dfc05c1a7f9f9cf620187547781111da6ad08ab) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='categorical_lupmf' href='#categorical_lupmf' class='anchored unlink'>**categorical_lupmf**:</a>
- <div class='index-container'>[`(ints y | vector theta) : real`](bounded_discrete_distributions.qmd#index-entry-83c502e2e302199ed3e04bed34c4bef07808ba9d) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='categorical_rng' href='#categorical_rng' class='anchored unlink'>**categorical_rng**:</a>
- <div class='index-container'>[`(vector theta) : int`](bounded_discrete_distributions.qmd#index-entry-e829b16f14961a0a24d2dd1a7895dcda4ce79bd1) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='cauchy' href='#cauchy' class='anchored unlink'>**cauchy**:</a>
- <div class='index-container'>[distribution statement](unbounded_continuous_distributions.qmd#index-entry-4e9a3b08fddc23e306b5a3b0a4f199124cb7cd90) <span class='detail'>(unbounded_continuous_distributions.html)</span></div>
<a id='cauchy_cdf' href='#cauchy_cdf' class='anchored unlink'>**cauchy_cdf**:</a>
- <div class='index-container'>[`(reals y | reals mu, reals sigma) : real`](unbounded_continuous_distributions.qmd#index-entry-f636bb8d19bdc544f177d76c3e93b11a8947a332) <span class='detail'>(unbounded_continuous_distributions.html)</span></div>
<a id='cauchy_lccdf' href='#cauchy_lccdf' class='anchored unlink'>**cauchy_lccdf**:</a>
- <div class='index-container'>[`(reals y | reals mu, reals sigma) : real`](unbounded_continuous_distributions.qmd#index-entry-252fde132b94e629570349d740a553001ba151d7) <span class='detail'>(unbounded_continuous_distributions.html)</span></div>
<a id='cauchy_lcdf' href='#cauchy_lcdf' class='anchored unlink'>**cauchy_lcdf**:</a>
- <div class='index-container'>[`(reals y | reals mu, reals sigma) : real`](unbounded_continuous_distributions.qmd#index-entry-1470e53e1ef3170600faa1e10925e17becd26f46) <span class='detail'>(unbounded_continuous_distributions.html)</span></div>
<a id='cauchy_lpdf' href='#cauchy_lpdf' class='anchored unlink'>**cauchy_lpdf**:</a>
- <div class='index-container'>[`(reals y | reals mu, reals sigma) : real`](unbounded_continuous_distributions.qmd#index-entry-365b2742adf729c8087f3eb28841c38baec29082) <span class='detail'>(unbounded_continuous_distributions.html)</span></div>
<a id='cauchy_lupdf' href='#cauchy_lupdf' class='anchored unlink'>**cauchy_lupdf**:</a>
- <div class='index-container'>[`(reals y | reals mu, reals sigma) : real`](unbounded_continuous_distributions.qmd#index-entry-70ded17908d0eaf198cca69f74a0bec65a4ec897) <span class='detail'>(unbounded_continuous_distributions.html)</span></div>
<a id='cauchy_rng' href='#cauchy_rng' class='anchored unlink'>**cauchy_rng**:</a>
- <div class='index-container'>[`(reals mu, reals sigma) : R`](unbounded_continuous_distributions.qmd#index-entry-56d08e840245967636a7f56a3b26cf0ad54161f8) <span class='detail'>(unbounded_continuous_distributions.html)</span></div>
<a id='cbrt' href='#cbrt' class='anchored unlink'>**cbrt**:</a>
- <div class='index-container'>[`(T x) : R`](real-valued_basic_functions.qmd#index-entry-e5c3ef31b3dfc2b73c3572239e82a2ae8629df79) <span class='detail'>(real-valued_basic_functions.html)</span></div>
<a id='ceil' href='#ceil' class='anchored unlink'>**ceil**:</a>
- <div class='index-container'>[`(T x) : R`](real-valued_basic_functions.qmd#index-entry-3989753a963097381576ca0373b3190681b0bbe8) <span class='detail'>(real-valued_basic_functions.html)</span></div>
<a id='chi_square' href='#chi_square' class='anchored unlink'>**chi_square**:</a>
- <div class='index-container'>[distribution statement](positive_continuous_distributions.qmd#index-entry-a8bd60e9ff005e8522863542e28a64336a42e65c) <span class='detail'>(positive_continuous_distributions.html)</span></div>
<a id='chi_square_cdf' href='#chi_square_cdf' class='anchored unlink'>**chi_square_cdf**:</a>
- <div class='index-container'>[`(reals y | reals nu) : real`](positive_continuous_distributions.qmd#index-entry-face5eba84183b72541fdba1f3b6ea4a1949e9b5) <span class='detail'>(positive_continuous_distributions.html)</span></div>
<a id='chi_square_lccdf' href='#chi_square_lccdf' class='anchored unlink'>**chi_square_lccdf**:</a>
- <div class='index-container'>[`(reals y | reals nu) : real`](positive_continuous_distributions.qmd#index-entry-a010e1cf6b0229303867a826777cc2a9b6c3bff9) <span class='detail'>(positive_continuous_distributions.html)</span></div>
<a id='chi_square_lcdf' href='#chi_square_lcdf' class='anchored unlink'>**chi_square_lcdf**:</a>
- <div class='index-container'>[`(reals y | reals nu) : real`](positive_continuous_distributions.qmd#index-entry-90d49c25cb5546006ff8802e5928c09d11c03dc8) <span class='detail'>(positive_continuous_distributions.html)</span></div>
<a id='chi_square_lpdf' href='#chi_square_lpdf' class='anchored unlink'>**chi_square_lpdf**:</a>
- <div class='index-container'>[`(reals y | reals nu) : real`](positive_continuous_distributions.qmd#index-entry-6c7045c1cb405776f7ed13ebbb5da4b27240ea15) <span class='detail'>(positive_continuous_distributions.html)</span></div>
<a id='chi_square_lupdf' href='#chi_square_lupdf' class='anchored unlink'>**chi_square_lupdf**:</a>
- <div class='index-container'>[`(reals y | reals nu) : real`](positive_continuous_distributions.qmd#index-entry-9cccc8fcca1c8dd1b172176bd72c946a84d611eb) <span class='detail'>(positive_continuous_distributions.html)</span></div>
<a id='chi_square_rng' href='#chi_square_rng' class='anchored unlink'>**chi_square_rng**:</a>
- <div class='index-container'>[`(reals nu) : R`](positive_continuous_distributions.qmd#index-entry-ced9b4410298033c3bdae65b66331f4a6d973c89) <span class='detail'>(positive_continuous_distributions.html)</span></div>
<a id='chol2inv' href='#chol2inv' class='anchored unlink'>**chol2inv**:</a>
- <div class='index-container'>[`(matrix L) : matrix`](matrix_operations.qmd#index-entry-0fbf0fe61f7df06da84a357eb40e9c719ff806ac) <span class='detail'>(matrix_operations.html)</span></div>
<a id='cholesky_decompose' href='#cholesky_decompose' class='anchored unlink'>**cholesky_decompose**:</a>
- <div class='index-container'>[`(matrix A) : matrix`](matrix_operations.qmd#index-entry-a7eaa217876baa0054d78dfff05f5685ef6261bb) <span class='detail'>(matrix_operations.html)</span></div>
<a id='choose' href='#choose' class='anchored unlink'>**choose**:</a>
- <div class='index-container'>[`(int x, int y) : int`](real-valued_basic_functions.qmd#index-entry-fd4d9124ce89bf38a7ca1601e28f14947fcae3ba) <span class='detail'>(real-valued_basic_functions.html)</span></div>
- <div class='index-container'>[`(T1 x, T2 y) : R`](real-valued_basic_functions.qmd#index-entry-ed9d9ccf90b8976a4cc2b40babee7c60d4807087) <span class='detail'>(real-valued_basic_functions.html)</span></div>
<a id='col' href='#col' class='anchored unlink'>**col**:</a>
- <div class='index-container'>[`(complex_matrix x, int n) : complex_vector`](complex_matrix_operations.qmd#index-entry-3a0cf3be0b3793d63afbee36001fbeed1f83f08f) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(matrix x, int n) : vector`](matrix_operations.qmd#index-entry-fe3819da259646140d101538903c86c5bc1b49e9) <span class='detail'>(matrix_operations.html)</span></div>
<a id='cols' href='#cols' class='anchored unlink'>**cols**:</a>
- <div class='index-container'>[`(complex_matrix x) : int`](complex_matrix_operations.qmd#index-entry-22eb74ccaa0e3cbd1875a10b1d25e448aaca1078) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(complex_row_vector x) : int`](complex_matrix_operations.qmd#index-entry-a3afb9b9b85c96fcbb2ceccffe8220cdf6930ee0) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(complex_vector x) : int`](complex_matrix_operations.qmd#index-entry-2926894bc112a2f76fc88ec0d1b66ca72f6907ab) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(matrix x) : int`](matrix_operations.qmd#index-entry-f399f6ffab24708be4ff867cbaef541158fc00bf) <span class='detail'>(matrix_operations.html)</span></div>
- <div class='index-container'>[`(row_vector x) : int`](matrix_operations.qmd#index-entry-417aeef6881030f640a4ea077e02335739bf0e3e) <span class='detail'>(matrix_operations.html)</span></div>
- <div class='index-container'>[`(vector x) : int`](matrix_operations.qmd#index-entry-8113ac540f4cc3aa182c3afcfa5d1665778f7fd9) <span class='detail'>(matrix_operations.html)</span></div>
<a id='columns_dot_product' href='#columns_dot_product' class='anchored unlink'>**columns_dot_product**:</a>
- <div class='index-container'>[`(complex_matrix x, complex_matrix y) : complex_row_vector`](complex_matrix_operations.qmd#index-entry-c0a3895052c73d4b7553b42dfbcf4ceee17d6ebd) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(complex_row_vector x, complex_row_vector y) : complex_row_vector`](complex_matrix_operations.qmd#index-entry-aee28160ebf0573187fba8d1b9917b490dfd47cd) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(complex_vector x, complex_vector y) : complex_row_vector`](complex_matrix_operations.qmd#index-entry-73c167059a6fb3ee21b48776d84d7c14cd6b6b9a) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(matrix x, matrix y) : row_vector`](matrix_operations.qmd#index-entry-758593f0bee7c0421df7fc503237288851879118) <span class='detail'>(matrix_operations.html)</span></div>
- <div class='index-container'>[`(row_vector x, row_vector y) : row_vector`](matrix_operations.qmd#index-entry-4758c18c6242ed86d28834ea3c356de1d5e22b86) <span class='detail'>(matrix_operations.html)</span></div>
- <div class='index-container'>[`(vector x, vector y) : row_vector`](matrix_operations.qmd#index-entry-7b3a4d9f9236657fd6d5970b8840e4a2e7e176bf) <span class='detail'>(matrix_operations.html)</span></div>
<a id='columns_dot_self' href='#columns_dot_self' class='anchored unlink'>**columns_dot_self**:</a>
- <div class='index-container'>[`(complex_matrix x) : complex_row_vector`](complex_matrix_operations.qmd#index-entry-499a93465efa4feea0949bffdec099ac446865be) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(complex_row_vector x) : complex_row_vector`](complex_matrix_operations.qmd#index-entry-5a3c0ca6ac56df87695d6d53c5ed41bd076db1bf) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(complex_vector x) : complex_row_vector`](complex_matrix_operations.qmd#index-entry-25320510319f7efaed97fc7327bcb3481a1fd055) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(matrix x) : row_vector`](matrix_operations.qmd#index-entry-664db2ea209dd84f3f62d813817a0be019ff3afb) <span class='detail'>(matrix_operations.html)</span></div>
- <div class='index-container'>[`(row_vector x) : row_vector`](matrix_operations.qmd#index-entry-258f64fdc22d8a6e1012cfa375d94222962c3add) <span class='detail'>(matrix_operations.html)</span></div>
- <div class='index-container'>[`(vector x) : row_vector`](matrix_operations.qmd#index-entry-f0c5a660d69d25748bdafa9cda98ee0cfa190cbe) <span class='detail'>(matrix_operations.html)</span></div>
<a id='complex_schur_decompose' href='#complex_schur_decompose' class='anchored unlink'>**complex_schur_decompose**:</a>
- <div class='index-container'>[`(complex_matrix A) : tuple(complex_matrix, complex_matrix)`](complex_matrix_operations.qmd#index-entry-400ef877200b32483b4f5a7223c3231666d153b7) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(matrix A) : tuple(complex_matrix, complex_matrix)`](complex_matrix_operations.qmd#index-entry-9c45b8917b1de6f500415512b1d06896cd5f7b5c) <span class='detail'>(complex_matrix_operations.html)</span></div>
<a id='complex_schur_decompose_t' href='#complex_schur_decompose_t' class='anchored unlink'>**complex_schur_decompose_t**:</a>
- <div class='index-container'>[`(complex_matrix A) : complex_matrix`](complex_matrix_operations.qmd#index-entry-1728988d586fc721b7a1d7d21d1aa3252bb03f94) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(matrix A) : complex_matrix`](complex_matrix_operations.qmd#index-entry-f43e2c8a9893e96b7c09a618d7b6f69350bfc460) <span class='detail'>(complex_matrix_operations.html)</span></div>
<a id='complex_schur_decompose_u' href='#complex_schur_decompose_u' class='anchored unlink'>**complex_schur_decompose_u**:</a>
- <div class='index-container'>[`(complex_matrix A) : complex_matrix`](complex_matrix_operations.qmd#index-entry-fdc477180371e8366e3a46dc88f3875f088907c8) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(matrix A) : complex_matrix`](complex_matrix_operations.qmd#index-entry-b169076e82ada507c5c30f36fe4a5bda58af9e0a) <span class='detail'>(complex_matrix_operations.html)</span></div>
<a id='conj' href='#conj' class='anchored unlink'>**conj**:</a>
- <div class='index-container'>[`(complex z) : complex`](complex-valued_basic_functions.qmd#index-entry-bd2ae18bb245caf34d1b2f12b3883c47d8aa7e0a) <span class='detail'>(complex-valued_basic_functions.html)</span></div>
- <div class='index-container'>[`(Z z) : Z`](complex-valued_basic_functions.qmd#index-entry-17692d922273aaba0c5317617aab6585dda28bfa) <span class='detail'>(complex-valued_basic_functions.html)</span></div>
<a id='cos' href='#cos' class='anchored unlink'>**cos**:</a>
- <div class='index-container'>[`(complex z) : complex`](complex-valued_basic_functions.qmd#index-entry-3d86aa681cf64514f405ada706ad9969e5f33080) <span class='detail'>(complex-valued_basic_functions.html)</span></div>
- <div class='index-container'>[`(T x) : R`](real-valued_basic_functions.qmd#index-entry-c587dc7908ecfe46cdd09800844ad9ea90e8463b) <span class='detail'>(real-valued_basic_functions.html)</span></div>
<a id='cosh' href='#cosh' class='anchored unlink'>**cosh**:</a>
- <div class='index-container'>[`(complex z) : complex`](complex-valued_basic_functions.qmd#index-entry-9b0fa15f5eebadc83a3678cb57fd8a1f4d089b94) <span class='detail'>(complex-valued_basic_functions.html)</span></div>
- <div class='index-container'>[`(T x) : R`](real-valued_basic_functions.qmd#index-entry-1afe4d43c0f158ff3446b0459e002ad8343ee24e) <span class='detail'>(real-valued_basic_functions.html)</span></div>
<a id='cov_exp_quad' href='#cov_exp_quad' class='anchored unlink'>**cov_exp_quad**:</a>
- <div class='index-container'>[`(array[] real x, real alpha, real rho) : matrix`](removed_functions.qmd#index-entry-1ba90fc13ad6ba28ca73fc3b94b0a65af09669f8) <span class='detail'>(removed_functions.html)</span></div>
- <div class='index-container'>[`(array[] real x1, array[] real x2, real alpha, real rho) : matrix`](removed_functions.qmd#index-entry-95bfeb84294b276027c24d3f8856560234423e7c) <span class='detail'>(removed_functions.html)</span></div>
- <div class='index-container'>[`(row_vectors x, real alpha, real rho) : matrix`](removed_functions.qmd#index-entry-92099ecf9309d8f643e455cb6e3f79c985d35cb1) <span class='detail'>(removed_functions.html)</span></div>
- <div class='index-container'>[`(row_vectors x1, row_vectors x2, real alpha, real rho) : matrix`](removed_functions.qmd#index-entry-c05741ae8e35d6b11a03c0098ac00b99d5a5c845) <span class='detail'>(removed_functions.html)</span></div>
- <div class='index-container'>[`(vectors x, real alpha, real rho) : matrix`](removed_functions.qmd#index-entry-d271045bb5d0614ff3a2f0e3d8d279d134cf0304) <span class='detail'>(removed_functions.html)</span></div>
- <div class='index-container'>[`(vectors x1, vectors x2, real alpha, real rho) : matrix`](removed_functions.qmd#index-entry-70b15de7e29e4e64f05ca3fc552da349d4a66c1f) <span class='detail'>(removed_functions.html)</span></div>
<a id='crossprod' href='#crossprod' class='anchored unlink'>**crossprod**:</a>
- <div class='index-container'>[`(matrix x) : matrix`](matrix_operations.qmd#index-entry-c5372c9d5715e11b5d87a465d6d671d608ef9513) <span class='detail'>(matrix_operations.html)</span></div>
<a id='csr_extract' href='#csr_extract' class='anchored unlink'>**csr_extract**:</a>
- <div class='index-container'>[`(matrix a) : tuple(vector, array[] int, array[] int)`](sparse_matrix_operations.qmd#index-entry-32fea6602ecbd4c1ea15d25bb2a6b2d2fcf58e52) <span class='detail'>(sparse_matrix_operations.html)</span></div>
<a id='csr_extract_u' href='#csr_extract_u' class='anchored unlink'>**csr_extract_u**:</a>
- <div class='index-container'>[`(matrix a) : array[] int`](sparse_matrix_operations.qmd#index-entry-1f750e4b73b9d17d5eadd184840443bab5de2dda) <span class='detail'>(sparse_matrix_operations.html)</span></div>
<a id='csr_extract_v' href='#csr_extract_v' class='anchored unlink'>**csr_extract_v**:</a>
- <div class='index-container'>[`(matrix a) : array[] int`](sparse_matrix_operations.qmd#index-entry-2569af86a359f94d59f18b21a0b4a15d7ad13f5f) <span class='detail'>(sparse_matrix_operations.html)</span></div>
<a id='csr_extract_w' href='#csr_extract_w' class='anchored unlink'>**csr_extract_w**:</a>
- <div class='index-container'>[`(matrix a) : vector`](sparse_matrix_operations.qmd#index-entry-fa08d7d6e24c28fcab7d2276501e5cbf1b12e09d) <span class='detail'>(sparse_matrix_operations.html)</span></div>
<a id='csr_matrix_times_vector' href='#csr_matrix_times_vector' class='anchored unlink'>**csr_matrix_times_vector**:</a>
- <div class='index-container'>[`(int m, int n, vector w, array[] int v, array[] int u, vector b) : vector`](sparse_matrix_operations.qmd#index-entry-a5e3d826290e2d8bff8cf1e1019bd2656ad43d2b) <span class='detail'>(sparse_matrix_operations.html)</span></div>
<a id='csr_to_dense_matrix' href='#csr_to_dense_matrix' class='anchored unlink'>**csr_to_dense_matrix**:</a>
- <div class='index-container'>[`(int m, int n, vector w, array[] int v, array[] int u) : matrix`](sparse_matrix_operations.qmd#index-entry-b8ce33cfed90d588aaa17f7c95c10b4206863d15) <span class='detail'>(sparse_matrix_operations.html)</span></div>
<a id='cumulative_sum' href='#cumulative_sum' class='anchored unlink'>**cumulative_sum**:</a>
- <div class='index-container'>[`(array[] complex x) : array[] complex`](complex_matrix_operations.qmd#index-entry-d6b4157abb8f1f7140f20c5b9182ad2f7d69fe37) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(array[] int x) : array[] int`](matrix_operations.qmd#index-entry-092f8a13b9e06f8346cb61b8fc6a6fbacb3b5cc5) <span class='detail'>(matrix_operations.html)</span></div>
- <div class='index-container'>[`(array[] real x) : array[] real`](matrix_operations.qmd#index-entry-1e965776faac7516107384178cafd382f87f909a) <span class='detail'>(matrix_operations.html)</span></div>
- <div class='index-container'>[`(complex_row_vector rv) : complex_row_vector`](complex_matrix_operations.qmd#index-entry-c104f0e3e10596f559a8a023c84f92f1b919bc0f) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(complex_vector v) : complex_vector`](complex_matrix_operations.qmd#index-entry-45545f14726c28e6b63c8ec09e06e53b33e4ca02) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(row_vector rv) : row_vector`](matrix_operations.qmd#index-entry-951e3c465251f531a70f0dce6772057bf114685c) <span class='detail'>(matrix_operations.html)</span></div>
- <div class='index-container'>[`(vector v) : vector`](matrix_operations.qmd#index-entry-7c00c2971c29f98a54f16c9468d5b4a6eb529ff8) <span class='detail'>(matrix_operations.html)</span></div>
## D
<a id='dae' href='#dae' class='anchored unlink'>**dae**:</a>
- <div class='index-container'>[`(function residual, vector initial_state, vector initial_state_derivative, data real initial_time, data array[] real times, ...) : array[] vector`](higher-order_functions.qmd#index-entry-c47e85b0ae801c7df44337e2c2b7ffc5c84037bf) <span class='detail'>(higher-order_functions.html)</span></div>
<a id='dae_tol' href='#dae_tol' class='anchored unlink'>**dae_tol**:</a>
- <div class='index-container'>[`(function residual, vector initial_state, vector initial_state_derivative, data real initial_time, data array[] real times, data real rel_tol, data real abs_tol, int max_num_steps, ...) : array[] vector`](higher-order_functions.qmd#index-entry-52f7e7ef9a4a58eb94353bf2cb98511deb94aac9) <span class='detail'>(higher-order_functions.html)</span></div>
<a id='determinant' href='#determinant' class='anchored unlink'>**determinant**:</a>
- <div class='index-container'>[`(matrix A) : real`](matrix_operations.qmd#index-entry-2f0c697d96cb41a09f35f183f179f15b1ee0f3fa) <span class='detail'>(matrix_operations.html)</span></div>
<a id='diag_matrix' href='#diag_matrix' class='anchored unlink'>**diag_matrix**:</a>
- <div class='index-container'>[`(complex_vector x) : complex_matrix`](complex_matrix_operations.qmd#index-entry-06edc5538b52d1a11f2a6f45be9ca1e0683bbb1e) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(vector x) : matrix`](matrix_operations.qmd#index-entry-74845a2c2d1e1321f2bfdf69d4c7f321c856f555) <span class='detail'>(matrix_operations.html)</span></div>
<a id='diag_post_multiply' href='#diag_post_multiply' class='anchored unlink'>**diag_post_multiply**:</a>
- <div class='index-container'>[`(complex_matrix m, complex_row_vector v) : complex_matrix`](complex_matrix_operations.qmd#index-entry-82629e9f9045325a28b4c0610df36226bc6c4562) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(complex_matrix m, complex_vector v) : complex_matrix`](complex_matrix_operations.qmd#index-entry-b8e527d5b7adcfe81f12d70984ba81d895332835) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(matrix m, row_vector rv) : matrix`](matrix_operations.qmd#index-entry-fedf6c86ebf0663043f5e986e077701e6ae185f4) <span class='detail'>(matrix_operations.html)</span></div>
- <div class='index-container'>[`(matrix m, vector v) : matrix`](matrix_operations.qmd#index-entry-2ff483d0f2d35ce6055a030912e1909c110453dc) <span class='detail'>(matrix_operations.html)</span></div>
<a id='diag_pre_multiply' href='#diag_pre_multiply' class='anchored unlink'>**diag_pre_multiply**:</a>
- <div class='index-container'>[`(complex_row_vector v, complex_matrix m) : complex_matrix`](complex_matrix_operations.qmd#index-entry-29b61ea8d42d42252259e35dbe0c427c485ad9e8) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(complex_vector v, complex_matrix m) : complex_matrix`](complex_matrix_operations.qmd#index-entry-7907eb3baed066d578933e3832fe8366c02116eb) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(row_vector rv, matrix m) : matrix`](matrix_operations.qmd#index-entry-87b1033ce509f3990ef4516c29c0b9b08d67c37b) <span class='detail'>(matrix_operations.html)</span></div>
- <div class='index-container'>[`(vector v, matrix m) : matrix`](matrix_operations.qmd#index-entry-0fc4d71e7bc087ce4f9dec77e1df8df248f41bac) <span class='detail'>(matrix_operations.html)</span></div>
<a id='diagonal' href='#diagonal' class='anchored unlink'>**diagonal**:</a>
- <div class='index-container'>[`(complex_matrix x) : complex_vector`](complex_matrix_operations.qmd#index-entry-5d28ae699b02999166db3502cec1f2c9b74d1c34) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(matrix x) : vector`](matrix_operations.qmd#index-entry-6d4ef3406b8dabab1d53b29bb53ae58d983d1404) <span class='detail'>(matrix_operations.html)</span></div>
<a id='digamma' href='#digamma' class='anchored unlink'>**digamma**:</a>
- <div class='index-container'>[`(T x) : R`](real-valued_basic_functions.qmd#index-entry-2ce1d8a0cdd9878fe64366c88a2381d6e702ff7d) <span class='detail'>(real-valued_basic_functions.html)</span></div>
<a id='dims' href='#dims' class='anchored unlink'>**dims**:</a>
- <div class='index-container'>[`(T x) : array[] int`](array_operations.qmd#index-entry-15460652371e3354bdc590e3632fc540ab76b525) <span class='detail'>(array_operations.html)</span></div>
<a id='dirichlet' href='#dirichlet' class='anchored unlink'>**dirichlet**:</a>
- <div class='index-container'>[distribution statement](simplex_distributions.qmd#index-entry-2b1866f861130d47e076c909b2da014d36b08615) <span class='detail'>(simplex_distributions.html)</span></div>
<a id='dirichlet_lpdf' href='#dirichlet_lpdf' class='anchored unlink'>**dirichlet_lpdf**:</a>
- <div class='index-container'>[`(vectors theta | vectors alpha) : real`](simplex_distributions.qmd#index-entry-912dbafe0e9fce423e5413cf88d46731b610742d) <span class='detail'>(simplex_distributions.html)</span></div>
<a id='dirichlet_lupdf' href='#dirichlet_lupdf' class='anchored unlink'>**dirichlet_lupdf**:</a>
- <div class='index-container'>[`(vectors theta | vectors alpha) : real`](simplex_distributions.qmd#index-entry-d287f450cfac7ef63c57f921d82484ef44abdfa0) <span class='detail'>(simplex_distributions.html)</span></div>
<a id='dirichlet_multinomial' href='#dirichlet_multinomial' class='anchored unlink'>**dirichlet_multinomial**:</a>
- <div class='index-container'>[distribution statement](multivariate_discrete_distributions.qmd#index-entry-3f5317d36179306fa3d125648b669c29f0ae4632) <span class='detail'>(multivariate_discrete_distributions.html)</span></div>
<a id='dirichlet_multinomial_lpmf' href='#dirichlet_multinomial_lpmf' class='anchored unlink'>**dirichlet_multinomial_lpmf**:</a>
- <div class='index-container'>[`(array[] int y | vector alpha) : real`](multivariate_discrete_distributions.qmd#index-entry-fdad801bbd6eb934645dbde5c01f271aa4e741b4) <span class='detail'>(multivariate_discrete_distributions.html)</span></div>
<a id='dirichlet_multinomial_lupmf' href='#dirichlet_multinomial_lupmf' class='anchored unlink'>**dirichlet_multinomial_lupmf**:</a>
- <div class='index-container'>[`(array[] int y | vector alpha) : real`](multivariate_discrete_distributions.qmd#index-entry-6b8a21266747ae90543cbd60108ee12b4d08d5e3) <span class='detail'>(multivariate_discrete_distributions.html)</span></div>
<a id='dirichlet_multinomial_rng' href='#dirichlet_multinomial_rng' class='anchored unlink'>**dirichlet_multinomial_rng**:</a>
- <div class='index-container'>[`(vector alpha, int N) : array[] int`](multivariate_discrete_distributions.qmd#index-entry-bdd1be0680f9ae13a49c9c4e6af87b4f9c7359df) <span class='detail'>(multivariate_discrete_distributions.html)</span></div>
<a id='dirichlet_rng' href='#dirichlet_rng' class='anchored unlink'>**dirichlet_rng**:</a>
- <div class='index-container'>[`(vector alpha) : vector`](simplex_distributions.qmd#index-entry-055ed033fb2096aa99f68c19fe9c3a956577f3b1) <span class='detail'>(simplex_distributions.html)</span></div>
<a id='discrete_range' href='#discrete_range' class='anchored unlink'>**discrete_range**:</a>
- <div class='index-container'>[distribution statement](bounded_discrete_distributions.qmd#index-entry-081a4566d9bb14c20636b30012e90be941b53978) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='discrete_range_cdf' href='#discrete_range_cdf' class='anchored unlink'>**discrete_range_cdf**:</a>
- <div class='index-container'>[`(ints y | ints l, ints u) : real`](bounded_discrete_distributions.qmd#index-entry-92d375a0144eecf4c3bac183f06cde0a573ae0ef) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='discrete_range_lccdf' href='#discrete_range_lccdf' class='anchored unlink'>**discrete_range_lccdf**:</a>
- <div class='index-container'>[`(ints y | ints l, ints u) : real`](bounded_discrete_distributions.qmd#index-entry-3dc029db4d1f37e783107470ba6665c647f5a202) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='discrete_range_lcdf' href='#discrete_range_lcdf' class='anchored unlink'>**discrete_range_lcdf**:</a>
- <div class='index-container'>[`(ints y | ints l, ints u) : real`](bounded_discrete_distributions.qmd#index-entry-be12560a3a7c198ea965f08a78dab04d83742159) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='discrete_range_lpmf' href='#discrete_range_lpmf' class='anchored unlink'>**discrete_range_lpmf**:</a>
- <div class='index-container'>[`(ints y | ints l, ints u) : real`](bounded_discrete_distributions.qmd#index-entry-4aeab4cc5d644e56b9409bff2224f5e620c7ce53) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='discrete_range_lupmf' href='#discrete_range_lupmf' class='anchored unlink'>**discrete_range_lupmf**:</a>
- <div class='index-container'>[`(ints y | ints l, ints u) : real`](bounded_discrete_distributions.qmd#index-entry-32514432b1689ab58c658ff3b435675a6e798cef) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='discrete_range_rng' href='#discrete_range_rng' class='anchored unlink'>**discrete_range_rng**:</a>
- <div class='index-container'>[`(ints l, ints u) : ints`](bounded_discrete_distributions.qmd#index-entry-a4c6bdebab12a3547ca7c13ac62e456d0b74c9dc) <span class='detail'>(bounded_discrete_distributions.html)</span></div>
<a id='distance' href='#distance' class='anchored unlink'>**distance**:</a>
- <div class='index-container'>[`(row_vector x, row_vector y) : real`](array_operations.qmd#index-entry-c6112c85adc9432ce6b005aff57babec0dbee55e) <span class='detail'>(array_operations.html)</span></div>
- <div class='index-container'>[`(row_vector x, vector y) : real`](array_operations.qmd#index-entry-a9f701404655eb686e31e66d38918d7e08cd9f3b) <span class='detail'>(array_operations.html)</span></div>
- <div class='index-container'>[`(vector x, row_vector y) : real`](array_operations.qmd#index-entry-d68901fc0a3ff9e987854900a185ee2713e5c520) <span class='detail'>(array_operations.html)</span></div>
- <div class='index-container'>[`(vector x, vector y) : real`](array_operations.qmd#index-entry-702855e7be40e4fcfbe31b5f08538c5fbfba210e) <span class='detail'>(array_operations.html)</span></div>
<a id='dot_product' href='#dot_product' class='anchored unlink'>**dot_product**:</a>
- <div class='index-container'>[`(complex_row_vector x, complex_row_vector y) : complex`](complex_matrix_operations.qmd#index-entry-13cdb97ea7e259e98791362de8a261d17dab4e1c) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(complex_row_vector x, complex_vector y) : complex`](complex_matrix_operations.qmd#index-entry-d932a1eed6d525ce1077543b39b6834836923949) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(complex_vector x, complex_row_vector y) : complex`](complex_matrix_operations.qmd#index-entry-dd62ebed52c5e3210bb8a0155e1d5dfa70497439) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(complex_vector x, complex_vector y) : complex`](complex_matrix_operations.qmd#index-entry-bc037b34a4fdc977a944e39e9277f8e6c700bd5b) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(row_vector x, row_vector y) : real`](matrix_operations.qmd#index-entry-5fa1a043fd0dcebec0cb14fd09c1a965c33d37fe) <span class='detail'>(matrix_operations.html)</span></div>
- <div class='index-container'>[`(row_vector x, vector y) : real`](matrix_operations.qmd#index-entry-5624c84e1a33f2cf540a3d8a2994205918d9915c) <span class='detail'>(matrix_operations.html)</span></div>
- <div class='index-container'>[`(vector x, row_vector y) : real`](matrix_operations.qmd#index-entry-4ce3d3846b8c242984aca259fd01579e1b2179af) <span class='detail'>(matrix_operations.html)</span></div>
- <div class='index-container'>[`(vector x, vector y) : real`](matrix_operations.qmd#index-entry-6f3cb76e0af87d28bceef319e85e75976645662e) <span class='detail'>(matrix_operations.html)</span></div>
<a id='dot_self' href='#dot_self' class='anchored unlink'>**dot_self**:</a>
- <div class='index-container'>[`(complex_row_vector x) : complex`](complex_matrix_operations.qmd#index-entry-d0945f42b843344d7b22f5d088d229c5f5ba64bf) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(complex_vector x) : complex`](complex_matrix_operations.qmd#index-entry-1ae5feb968f94e219b01c1a6943eb1532161e16f) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(row_vector x) : real`](matrix_operations.qmd#index-entry-806eb76bdef36d3ee3a9a009027593ad32d755f1) <span class='detail'>(matrix_operations.html)</span></div>
- <div class='index-container'>[`(vector x) : real`](matrix_operations.qmd#index-entry-1ae4fbadff5f8d76241c1cfc33e2c36db7decc73) <span class='detail'>(matrix_operations.html)</span></div>
<a id='double_exponential' href='#double_exponential' class='anchored unlink'>**double_exponential**:</a>
- <div class='index-container'>[distribution statement](unbounded_continuous_distributions.qmd#index-entry-b3a44920aadcdd73a61301af6bfb0ba2be51abf8) <span class='detail'>(unbounded_continuous_distributions.html)</span></div>
<a id='double_exponential_cdf' href='#double_exponential_cdf' class='anchored unlink'>**double_exponential_cdf**:</a>
- <div class='index-container'>[`(reals y | reals mu, reals sigma) : real`](unbounded_continuous_distributions.qmd#index-entry-8339bce2e4f464e36cd18cd462828f0b740d2657) <span class='detail'>(unbounded_continuous_distributions.html)</span></div>
<a id='double_exponential_lccdf' href='#double_exponential_lccdf' class='anchored unlink'>**double_exponential_lccdf**:</a>
- <div class='index-container'>[`(reals y | reals mu, reals sigma) : real`](unbounded_continuous_distributions.qmd#index-entry-14eaa0ccbccd40ad1a210cba1462140349b9c18d) <span class='detail'>(unbounded_continuous_distributions.html)</span></div>
<a id='double_exponential_lcdf' href='#double_exponential_lcdf' class='anchored unlink'>**double_exponential_lcdf**:</a>
- <div class='index-container'>[`(reals y | reals mu, reals sigma) : real`](unbounded_continuous_distributions.qmd#index-entry-a77ae5c4ace742352452353b5faa44105bc79f55) <span class='detail'>(unbounded_continuous_distributions.html)</span></div>
<a id='double_exponential_lpdf' href='#double_exponential_lpdf' class='anchored unlink'>**double_exponential_lpdf**:</a>
- <div class='index-container'>[`(reals y | reals mu, reals sigma) : real`](unbounded_continuous_distributions.qmd#index-entry-f0eddd37cb58304271349b38fc0dc4de2aeb94f4) <span class='detail'>(unbounded_continuous_distributions.html)</span></div>
<a id='double_exponential_lupdf' href='#double_exponential_lupdf' class='anchored unlink'>**double_exponential_lupdf**:</a>
- <div class='index-container'>[`(reals y | reals mu, reals sigma) : real`](unbounded_continuous_distributions.qmd#index-entry-32427ca40b710f689e9f6f5f77ca5f91afc0ae09) <span class='detail'>(unbounded_continuous_distributions.html)</span></div>
<a id='double_exponential_rng' href='#double_exponential_rng' class='anchored unlink'>**double_exponential_rng**:</a>
- <div class='index-container'>[`(reals mu, reals sigma) : R`](unbounded_continuous_distributions.qmd#index-entry-5489a23aaef4c1953d0e22e808a68a6fc37ab1d8) <span class='detail'>(unbounded_continuous_distributions.html)</span></div>
## E
<a id='e' href='#e' class='anchored unlink'>**e**:</a>
- <div class='index-container'>[`() : real`](real-valued_basic_functions.qmd#index-entry-c9e1664eab4cc021df10c6902738cce047b7d8f8) <span class='detail'>(real-valued_basic_functions.html)</span></div>
<a id='eigendecompose' href='#eigendecompose' class='anchored unlink'>**eigendecompose**:</a>
- <div class='index-container'>[`(complex_matrix A) : tuple(complex_matrix, complex_vector)`](complex_matrix_operations.qmd#index-entry-cfb26916a57582e2e9ee4f68ed99c821756d3789) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(matrix A) : tuple(complex_matrix, complex_vector)`](matrix_operations.qmd#index-entry-080c58f8bf67678c670ce7454674192000c074d1) <span class='detail'>(matrix_operations.html)</span></div>
<a id='eigendecompose_sym' href='#eigendecompose_sym' class='anchored unlink'>**eigendecompose_sym**:</a>
- <div class='index-container'>[`(complex_matrix A) : tuple(complex_matrix, complex_vector)`](complex_matrix_operations.qmd#index-entry-2e32adea8a000a491b0d0d5e736075c377a776b6) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(matrix A) : tuple(matrix, vector)`](matrix_operations.qmd#index-entry-7bd20778cc4eb845435d980b2323a26d021c94a0) <span class='detail'>(matrix_operations.html)</span></div>
<a id='eigenvalues' href='#eigenvalues' class='anchored unlink'>**eigenvalues**:</a>
- <div class='index-container'>[`(complex_matrix A) : complex_vector`](complex_matrix_operations.qmd#index-entry-a3edb93c2a79b350e0e1ca880e3ada6deb6a30de) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(matrix A) : complex_vector`](matrix_operations.qmd#index-entry-db72fae33eaa940967d1488e046f1d41ad7bd7b7) <span class='detail'>(matrix_operations.html)</span></div>
<a id='eigenvalues_sym' href='#eigenvalues_sym' class='anchored unlink'>**eigenvalues_sym**:</a>
- <div class='index-container'>[`(complex_matrix A) : complex_vector`](complex_matrix_operations.qmd#index-entry-e271860ae502125255d5f4092244d884f2ce9692) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(matrix A) : vector`](matrix_operations.qmd#index-entry-09bb39cb077a959df51666f18ac7319ea53f8748) <span class='detail'>(matrix_operations.html)</span></div>
<a id='eigenvectors' href='#eigenvectors' class='anchored unlink'>**eigenvectors**:</a>
- <div class='index-container'>[`(complex_matrix A) : complex_matrix`](complex_matrix_operations.qmd#index-entry-bc7b059733d8c7e8becdef5196cfe34a63233de0) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(matrix A) : complex_matrix`](matrix_operations.qmd#index-entry-6c608598725ec7c838453abdeb440c875eafe1a5) <span class='detail'>(matrix_operations.html)</span></div>
<a id='eigenvectors_sym' href='#eigenvectors_sym' class='anchored unlink'>**eigenvectors_sym**:</a>
- <div class='index-container'>[`(complex_matrix A) : complex_matrix`](complex_matrix_operations.qmd#index-entry-67a04481d07493cc21dae09ba3cfde2b4e974951) <span class='detail'>(complex_matrix_operations.html)</span></div>
- <div class='index-container'>[`(matrix A) : matrix`](matrix_operations.qmd#index-entry-fb1919fccf8d3e19664c486e0cb67c876593f5a1) <span class='detail'>(matrix_operations.html)</span></div>
<a id='erf' href='#erf' class='anchored unlink'>**erf**:</a>
- <div class='index-container'>[`(T x) : R`](real-valued_basic_functions.qmd#index-entry-3ed55c0864c7839ec52fa38be9974f0e43bd5a50) <span class='detail'>(real-valued_basic_functions.html)</span></div>
<a id='erfc' href='#erfc' class='anchored unlink'>**erfc**:</a>
- <div class='index-container'>[`(T x) : R`](real-valued_basic_functions.qmd#index-entry-7dc68f18ec6e0c591f011d5ff8f4075637b9dd5c) <span class='detail'>(real-valued_basic_functions.html)</span></div>
<a id='exp' href='#exp' class='anchored unlink'>**exp**:</a>
- <div class='index-container'>[`(complex z) : complex`](complex-valued_basic_functions.qmd#index-entry-3c31357925206d6237b540fd4e33930d37dccb79) <span class='detail'>(complex-valued_basic_functions.html)</span></div>
- <div class='index-container'>[`(T x) : R`](real-valued_basic_functions.qmd#index-entry-f32e064beb0f00e975210d246d3f80431ea9b85f) <span class='detail'>(real-valued_basic_functions.html)</span></div>
<a id='exp2' href='#exp2' class='anchored unlink'>**exp2**:</a>
- <div class='index-container'>[`(T x) : R`](real-valued_basic_functions.qmd#index-entry-7db9b662f6846f90e9edf891fac2a64701c213d2) <span class='detail'>(real-valued_basic_functions.html)</span></div>
<a id='exp_mod_normal' href='#exp_mod_normal' class='anchored unlink'>**exp_mod_normal**:</a>
- <div class='index-container'>[distribution statement](unbounded_continuous_distributions.qmd#index-entry-b426ea4ba5c486f0dee2d11bcd8f019e1914e368) <span class='detail'>(unbounded_continuous_distributions.html)</span></div>
<a id='exp_mod_normal_cdf' href='#exp_mod_normal_cdf' class='anchored unlink'>**exp_mod_normal_cdf**:</a>
- <div class='index-container'>[`(reals y | reals mu, reals sigma, reals lambda) : real`](unbounded_continuous_distributions.qmd#index-entry-e60633c944fc492d9aabe37e92180634dc3beb1f) <span class='detail'>(unbounded_continuous_distributions.html)</span></div>