Skip to content

Commit

Permalink
Fix Gaussian distribution formula
Browse files Browse the repository at this point in the history
  • Loading branch information
moriglia committed Nov 14, 2024
1 parent 3369013 commit d9e6f3f
Showing 1 changed file with 2 additions and 2 deletions.
4 changes: 2 additions & 2 deletions doc/specs/stdlib_stats_distribution_normal.md
Original file line number Diff line number Diff line change
Expand Up @@ -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

Expand Down

0 comments on commit d9e6f3f

Please sign in to comment.