Skip to content

Commit

Permalink
Separated out numerical mean and variance from analytic
Browse files Browse the repository at this point in the history 
Added tests
rewrote equations in vignette
  • Loading branch information
@bertcarnell
bertcarnell committed Feb 4, 2024
1 parent 52cf2d5 commit 78ab7cd
Show file tree
Hide file tree
Showing 5 changed files with 290 additions and 102 deletions.
92 changes: 86 additions & 6 deletions R/mle.R
View file
Original file line number Diff line number Diff line change
Expand Up @@ -365,16 +365,34 @@ f_rth_order_stat <- function(x, n, r, a, b, c)
#'
#' @return the expected value
#'
#' @importFrom stats integrate
#' @examples
#' mean_rth_order_stat(10, 5, 0, 1, 0.5)
mean_rth_order_stat <- function(n, r, a, b, c)
{
integrand <- function(x, n, r, a, b, c) {x * f_rth_order_stat(x, n, r, a, b, c)}
stats::integrate(integrand, lower = a, upper = b, n = n, r = r, a = a, b = b, c = c)
# n <- 200
# r <- 100
# a <- 0
# b <- 1
# c <- 0.5
if (n > 10) {
return(mean_rth_order_stat_numeric(n, r, a, b, c))
} else {
coefs1 <- sapply(0:(n-r), function(k) {
choose(n-r, k) * (b-a)^(k-n) * (c-a)^{n-k} * (-1)^(n-r-k) *
(c/(n-k) - (c-a)/(n-k)/(2*n-2*k+1))
})

coefs2 <- sapply(0:(r-1), function(k) {
choose(r-1, k) * (b-a)^(k-n) * (c-b)^{n-k} *
(-c/(n-k) + (c-b)/(n-k)/(2*n-2*k+1))
})

return(ifelse(c > a, r*choose(n, r)*sum(coefs1), 0) +
ifelse(c < b, r*choose(n, r)*(-1)^(n-r)*sum(coefs2), 0))
}
}

#' Variance of the rth order statistic
#' Expected value of the rth order statistic using numeric integration
#'
#' @noRd
#'
Expand All @@ -388,13 +406,67 @@ mean_rth_order_stat <- function(n, r, a, b, c)
#'
#' @importFrom stats integrate
#' @examples
#' mean_rth_order_stat_numeric(10, 5, 0, 1, 0.5)
mean_rth_order_stat_numeric <- function(n, r, a, b, c)
{
integrand <- function(x, n, r, a, b, c) {x * f_rth_order_stat(x, n, r, a, b, c)}
stats::integrate(integrand, lower = a, upper = b, n = n, r = r, a = a, b = b, c = c)$value
}

#' Variance of the rth order statistic
#'
#' @noRd
#'
#' @param n number of order statistics
#' @param r the order statistic number
#' @param a the minimum support of the triangle distribution \code{a < b}, \code{a <= min(z)}
#' @param b the maximum support of the triangle distribution \code{b >= max(z)}
#' @param c the mode of the triangle distribution
#'
#' @return the variance
#'
#' @examples
#' variance_rth_order_stat(10, 5, 0, 1, 0.5)
variance_rth_order_stat <- function(n, r, a, b, c)
{
if (n > 10) {
variance_rth_order_stat_numeric(n, r, a, b, c)
} else {
coefs1 <- sapply(0:(n-r), function(k) {
choose(n-r, k) * (b-a)^(k-n) * (c-a)^(n-k) * (-1)^(n-r-k) / (n-k) *
(c^2 - 2*c*(c-a)/(2*n-2*k+1) + 2*(c-a)^2/(2*n-2*k+1)/(2*n-2*k+2))
})
coefs2 <- sapply(0:(r-1), function(k) {
choose(r-1, k) * (b-a)^(k-n) * (c-b)^(n-k)/(n-k) *
(-c^2 + 2*c*(c-b)/(2*n-2*k+1) - 2*(c-b)^2/(2*n-2*k+1)/(2*n-2*k+2))
})
m <- mean_rth_order_stat(n, r, a, b, c)
return(ifelse(c > a, r*choose(n, r)*sum(coefs1), 0) +
ifelse(c < b, r*choose(n, r)*(-1)^(n-r)*sum(coefs2), 0) - m^2)
}
}

#' Variance of the rth order statistic using numeric integration
#'
#' @noRd
#'
#' @param n number of order statistics
#' @param r the order statistic number
#' @param a the minimum support of the triangle distribution \code{a < b}, \code{a <= min(z)}
#' @param b the maximum support of the triangle distribution \code{b >= max(z)}
#' @param c the mode of the triangle distribution
#'
#' @return the variance
#'
#' @importFrom stats integrate
#' @examples
#' variance_rth_order_stat_numeric(10, 5, 0, 1, 0.5)
variance_rth_order_stat_numeric <- function(n, r, a, b, c)
{
integrand <- function(x, n, r, a, b, c) {x * x * f_rth_order_stat(x, n, r, a, b, c)}
E_x2 <- stats::integrate(integrand, lower = a, upper = b, n = n, r = r, a = a, b = b, c = c)
E_x <- mean_rth_order_stat(n, r, a, b, c)
E_x2$value - E_x$value * E_x$value
E_x <- mean_rth_order_stat_numeric(n, r, a, b, c)
E_x2$value - E_x * E_x
}

#' Maximum likelihood estimate of the triangle distribution parameters
Expand Down Expand Up @@ -450,6 +522,14 @@ triangle_mle <- function(x, debug = FALSE, maxiter = 100)
}

var_chat <- variance_rth_order_stat(length(x), mle_c2$r_hat, mle_ab$a, mle_ab$b, mle_c2$c_hat)
if (any(var_chat < 0) | debug) {
cat("\nNegative Varince in c hat\n")
cat("n=", length(x), "\n")
cat("r=", mle_c2$r_hat, "\n")
cat("a=", mle_ab$a, "\n")
cat("b=", mle_ab$b, "\n")
cat("c=", mle_c2$c_hat, "\n")
}
vcov <- rbind(cbind(solve(mle_ab$hessian_ab), c(0, 0)), c(0, 0, var_chat))
dimnames(vcov) <- list(c("a", "b", "c"), c("a", "b", "c"))

Expand Down
4 changes: 4 additions & 0 deletions tests/testthat/helper-mle-utils.R
View file
Original file line number Diff line number Diff line change
@@ -0,0 +1,4 @@
set.seed(39854)
xtest <- rtriangle(200, 0, 1, 0.5)

mle1 <- triangle_mle(xtest)
40 changes: 2 additions & 38 deletions tests/testthat/test-mle-utils.R
View file
Original file line number Diff line number Diff line change
@@ -1,8 +1,4 @@
test_that("summary works", {
set.seed(39854)
xtest <- rtriangle(200, 0, 1, 0.5)

mle1 <- triangle_mle(xtest)
summ <- summary(mle1)

expect_equal(summ@coef[,1], coef(mle1))
Expand All @@ -13,28 +9,16 @@ test_that("summary works", {
})

test_that("print works", {
set.seed(39854)
xtest <- rtriangle(200, 0, 1, 0.5)

mle1 <- triangle_mle(xtest)
expect_output(print(mle1))
})

test_that("coef works", {
set.seed(39854)
xtest <- rtriangle(200, 0, 1, 0.5)

mle1 <- triangle_mle(xtest)
cf <- coef(mle1)

expect_equal(mle1$coef, cf)
})

test_that("logLik works", {
set.seed(39854)
xtest <- rtriangle(200, 0, 1, 0.5)

mle1 <- triangle_mle(xtest)
ll <- logLik(mle1)

expect_equivalent(-1*nLL_triangle(xtest, mle1$coef[1], mle1$coef[2], mle1$coef[3]),
Expand All @@ -44,61 +28,41 @@ test_that("logLik works", {
})

test_that("AIC works", {
set.seed(39854)
xtest <- rtriangle(200, 0, 1, 0.5)

mle1 <- triangle_mle(xtest)
aic <- AIC(mle1)

expect_equivalent(2 * nLL_triangle(xtest, mle1$coef[1], mle1$coef[2], mle1$coef[3]) + 2 * 3,
aic)
})

test_that("BIC works", {
set.seed(39854)
xtest <- rtriangle(200, 0, 1, 0.5)

mle1 <- triangle_mle(xtest)
bic <- BIC(mle1)

expect_equivalent(2 * nLL_triangle(xtest, mle1$coef[1], mle1$coef[2], mle1$coef[3]) + log(length(xtest)) * 3,
bic)
})

test_that("vcov works", {
set.seed(39854)
xtest <- rtriangle(200, 0, 1, 0.5)

mle1 <- triangle_mle(xtest)
v <- vcov(mle1)

expect_equivalent(mle1$vcov, v)
})

test_that("profile works", {
set.seed(39854)
xtest <- rtriangle(200, 0, 1, 0.5)

mle1 <- triangle_mle(xtest)
prof <- profile(mle1)

expect_equivalent("profile.mle", class(prof))
expect_equal(3, length(prof@profile))
expect_equal(3, ncol(prof@profile$a$par.vals))

mle1 <- standard_triangle_mle(xtest)
prof <- profile(mle1)
mle2 <- standard_triangle_mle(xtest)
prof <- profile(mle2)

expect_equivalent("profile.mle", class(prof))
expect_equal(3, length(prof@profile))
expect_equal(3, ncol(prof@profile$a$par.vals))
})

test_that("confint works", {
set.seed(39854)
xtest <- rtriangle(200, 0, 1, 0.5)

mle1 <- triangle_mle(xtest)
cfi <- confint(mle1, level = 0.95)

expect_equal(c(3,2), dim(cfi))
Expand Down
37 changes: 32 additions & 5 deletions tests/testthat/test-mle.R
View file
Original file line number Diff line number Diff line change
Expand Up @@ -95,15 +95,31 @@ test_that("f_rth_order_stat works", {

test_that("mean_rth_order_stat works", {
temp <- mean_rth_order_stat(10, 5, 0, 1, 0.5)
expect_true(temp$value >= 0 & temp$value <= 1)
expect_true(temp$value < 0.5)
expect_true(temp >= 0 & temp <= 1)
expect_true(temp < 0.5)

temp <- mean_rth_order_stat(10, 6, 0, 1, 0.5)
expect_true(temp$value > 0.5)
expect_true(temp > 0.5)

temp <- mean_rth_order_stat(10, 1, 0, 1, 0.5)
expect_true(temp$value >= 0 & temp$value <= 1)
expect_true(temp >= 0 & temp <= 1)

temp <- mean_rth_order_stat(10, 10, 0, 1, 0.5)
expect_true(temp$value >= 0 & temp$value <= 1)
expect_true(temp >= 0 & temp <= 1)

expect_equal(mean_rth_order_stat_numeric(10, 5, 1, 3, 2),
mean_rth_order_stat(10, 5, 1, 3, 2), tolerance = 1E-6)
expect_equal(mean_rth_order_stat_numeric(10, 5, 1, 3, 1),
mean_rth_order_stat(10, 5, 1, 3, 1), tolerance = 1E-6)
expect_equal(mean_rth_order_stat_numeric(10, 5, 1, 3, 3),
mean_rth_order_stat(10, 5, 1, 3, 3), tolerance = 1E-6)
expect_equal(mean_rth_order_stat_numeric(10, 1, 1, 3, 2),
mean_rth_order_stat(10, 1, 1, 3, 2), tolerance = 1E-6)
expect_equal(mean_rth_order_stat_numeric(10, 10, 1, 3, 2),
mean_rth_order_stat(10, 10, 1, 3, 2), tolerance = 1E-4) ######

expect_true(mean_rth_order_stat(200, 100, 0, 1, 0.5) < 1)
expect_true(mean_rth_order_stat(200, 100, 0, 1, 0.5) > 0)
})

test_that("variance_rth_order_stat works", {
Expand All @@ -113,6 +129,17 @@ test_that("variance_rth_order_stat works", {
expect_true(variance_rth_order_stat(10, 8, 0, 1, 0.5) >= 0)
expect_true(variance_rth_order_stat(10, 9, 0, 1, 0.5) >= 0)
expect_true(variance_rth_order_stat(10, 10, 0, 1, 0.5) >= 0)

expect_equal(variance_rth_order_stat_numeric(10, 5, 1, 3, 2),
variance_rth_order_stat(10, 5, 1, 3, 2), tolerance = 1E-6)
expect_equal(variance_rth_order_stat_numeric(10, 5, 1, 3, 1),
variance_rth_order_stat(10, 5, 1, 3, 1), tolerance = 1E-6)
expect_equal(variance_rth_order_stat_numeric(10, 5, 1, 3, 3),
variance_rth_order_stat(10, 5, 1, 3, 3), tolerance = 1E-6)
expect_equal(variance_rth_order_stat_numeric(10, 1, 1, 3, 2),
variance_rth_order_stat(10, 1, 1, 3, 2), tolerance = 1E-6)
expect_equal(variance_rth_order_stat_numeric(10, 10, 1, 3, 2),
variance_rth_order_stat(10, 10, 1, 3, 2), tolerance = 1E-3) ####
})

test_that("triangle_mle works", {
Expand Down
Loading

0 comments on commit 78ab7cd

Please sign in to comment.