From 81d56dc71c9da9ebe2da230d36f1caf3acd14fec Mon Sep 17 00:00:00 2001 From: yh202109 Date: Fri, 12 Jul 2024 23:57:59 -0400 Subject: [PATCH] v0.2.20 --- docs/statlab_corr_spearman_rho.rst | 9 +++++---- 1 file changed, 5 insertions(+), 4 deletions(-) diff --git a/docs/statlab_corr_spearman_rho.rst b/docs/statlab_corr_spearman_rho.rst index 3dcbeb4c..730c8fe8 100644 --- a/docs/statlab_corr_spearman_rho.rst +++ b/docs/statlab_corr_spearman_rho.rst @@ -146,11 +146,11 @@ More Details ************* Assume that :math:`Y_{i1} \sim \mathcal{D}`. -In :eq:`eq_rank`, we defined :math:`R_{i1} = S_{i1} + \frac{S_{i2}+1}{2}`. +For continuous :math:`Y_{i1}`, if we can assume that :math:`P(S_{i2}=0)=1`, +then :eq:`eq_rank` can be simplified as :math:`R_{i1} = S_{i1}`. +For a given sample size :math:`n`, and :math:`r \in \{1, \ldots, n\}`, the PMF of :math:`R_{i1}` is +:math:`P(R_{i1} = r) = \frac{1}{n}`, which does not depend on :math:`\mathcal{D}` [4]_. -For continuous :math:`Y_{i1}`, if we can assume that :math:`P(S_{i2}=0)=1`, then :math:`R_{i1} = S_{i1}`. -For a given sample size :math:`n`, and :math:`r \in \{1, \ldots, n\}`, the pmf of :math:`R_{i1}` is -:math:`P(R_{i1} = r) = \frac{1}{n}`, which does not depend on :math:`\mathcal{D}`. ************* Reference @@ -159,4 +159,5 @@ Reference .. [1] Wikipedia. (year). Spearman's rank correlation coefficient. https://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient .. [2] julialang.org. (2022). Ranking of elements of a vector. https://discourse.julialang.org/t/ranking-of-elements-of-a-vector/88293/4 .. [3] scipy.org. (year). spearmanr. https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.spearmanr.html +.. [4] John Borkowski. (2014). Introduction to the Theory of Order Statistics and Rank Statistics. https://math.montana.edu/jobo/thainp/rankstat.pdf