# Talk:Normal distribution

## The Walsh Hadamard transform and the Normal Distribution

I eventually found this paper on using the Walsh Hadamard transform: [1] Wallace, C. S. 1996. "Fast Pseudorandom Generators for Normal and Exponential Variates." ACM Transactions on Mathematical Software.

I independently discovered the idea myself around 2001. I further showed that by combining the Walsh Hadamard transform with random permutations you can convert arbitrary numerical data into the Gaussian distribution. I am not sure if anyone has any prior claim to that. I have used it to create associative memory algorithms and as a population based method for generating random numbers for Evolutionary Strategies (ES) based algorithms. I am sure it would have other uses. A useful reference is [1] I am pretty sure NVidia got the idea from me (because I sent them an e-mail about it). They did however find the reference to Wallace which I could not find. Maybe you can still find some of my code on the forum of www.freebasic.net but a lot of it is gone from the Internet because no gain. Sean O'Connor

References

1. ^ Wallace, C.S. (1996). ACM Transactions on Mathematical Software: Fast Pseudorandom Generators for Normal and Exponential Variates. Missing or empty |title= (help)

## Bell Curve

I am sure this article is very good, but I came to this page to find out why a Bell curve (or bell curve) is called as it is. Is it named after a shape or the person who first devised it or what? And maybe the article should say so? Kiltpin (talk) 12:16, 27 October 2016 (UTC)

## Figure in "Standard deviation and coverage" section - vertical lines should be equally spaced

Hello, For the figure in the "Standard deviation and coverage" section, the vertical lines should be equally spaced. — Preceding unsigned comment added by 99.226.5.121 (talk) 21:31, 8 February 2017 (UTC)

This article is very good, clear citation, the math is correct, has very reliable references. But it doesn't mention that Gaussian Distribution has a widely application in air pollution transportation model and diffusion model. Jiamingshi (talk) 05:35, 28 April 2017 (UTC)

## At zero

Also the reciprocal of the standard deviation ${\displaystyle \tau ^{\prime }=1/\sigma }$ might be defined as the precision and the expression of the normal distribution becomes

${\displaystyle f(x)={\frac {\tau ^{\prime }}{\sqrt {2\pi }}}\,e^{-(\tau ^{\prime })^{2}(x-\mu )^{2}/2}.}$

According to Stigler, this formulation is advantageous because of a much simpler and easier-to-remember formula, the fact that the PDF has unit height at zero,

Well:

${\displaystyle f(0)={\frac {\tau ^{\prime }}{\sqrt {2\pi }}}\,e^{-(\tau ^{\prime })^{2}(0-\mu )^{2}/2}\neq 1}$ (in general)

and also for ${\displaystyle \tau =1,\mu =0}$

${\displaystyle f(0)={\frac {1}{\sqrt {2\pi }}}\,e^{0}\neq 1}$

So??? Madyno (talk) 15:04, 11 May 2017 (UTC)

## Quantile function

The section on the quantile function defines ${\displaystyle z_{p}}$ to be ${\displaystyle \Phi ^{-1}(p)}$, but then 2 lines later uses ${\displaystyle z_{p}}$ to mean something related but different, without warning.Fathead99 (talk) 15:17, 28 July 2017 (UTC)