From d9e6f3f6e87892b6f4054e1cb124236c8b7a1d7c Mon Sep 17 00:00:00 2001 From: Marco Origlia Date: Thu, 14 Nov 2024 15:11:40 +0100 Subject: [PATCH] Fix Gaussian distribution formula --- doc/specs/stdlib_stats_distribution_normal.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/doc/specs/stdlib_stats_distribution_normal.md b/doc/specs/stdlib_stats_distribution_normal.md index db32a3b60..7217171e3 100644 --- a/doc/specs/stdlib_stats_distribution_normal.md +++ b/doc/specs/stdlib_stats_distribution_normal.md @@ -64,11 +64,11 @@ Experimental The probability density function (pdf) of the single real variable normal distribution: -$$f(x) = \frac{1}{\sigma \sqrt{2}} \exp{\left[-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^{2}\right]}$$ +$$f(x) = \frac{1}{\sigma \sqrt{2\pi}} \exp{\left[-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^{2}\right]}$$ For a complex varible \( z=(x + y i) \) with independent real \( x \) and imaginary \( y \) parts, the joint probability density function is the product of the the corresponding real and imaginary marginal pdfs:[^2] -$$f(x + y \mathit{i}) = f(x) f(y) = \frac{1}{2\sigma_{x}\sigma_{y}} \exp{\left[-\frac{1}{2}\left(\left(\frac{x-\mu_x}{\sigma_{x}}\right)^{2}+\left(\frac{y-\mu_y}{\sigma_{y}}\right)^{2}\right)\right]}$$ +$$f(x + y \mathit{i}) = f(x) f(y) = \frac{1}{2\pi\sigma_{x}\sigma_{y}} \exp{\left[-\frac{1}{2}\left(\left(\frac{x-\mu_x}{\sigma_{x}}\right)^{2}+\left(\frac{y-\mu_y}{\sigma_{y}}\right)^{2}\right)\right]}$$ ### Syntax