Talk:Normal distribution

The Walsh Hadamard transform and the Normal Distribution

I eventually found this paper on using the Walsh Hadamard transform: 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

xo notation in Taylor Series sections

The statement says "... about any known value of the distribution, $\Phi (xo)$." Should $xo$ be $x_{0}$? Asyasylin (talk) 16:48, 17 April 2023 (UTC)

I think that that was supposed to be the case. This section also needs sources for verification. DekuNut64 (talk) 16:24, 22 April 2023 (UTC)

Needs to be simplified

Greetings Wikipedians! I salute the editors for all their work on this article. The effort must have been considerable, given the level of detail included here. But it seems to be written for math or engineering students, rather than for the average reader. It would benefit if someone would add a simple explanation that a layman can understand. The best place for that would be early in the article, prior to all those equations. I'll volunteer to correct that. As always, comments are welcome. Cordially, BuzzWeiser196 (talk) 15:50, 28 January 2024 (UTC)

Source Link Correction

Line 25 at References. The link to Encyclopedia of Mathematics is not correct, while the one in External links is right. I don't know the syntax of wiki. There someone to correct it? 不见槃极 (talk) 10:37, 14 June 2024 (UTC)

Confidence Intervals

Why are the confidence intervals all written/derived in terms of s² instead of the variance? Is this common in the literature? I feel it would be more consistent to use σ² throughout. For example, $$\sigma ^{2}\in \left[{\frac {n}{\chi _{n-1,1-\alpha /2}^{2}}}{\hat {\sigma }}^{2},\,{\frac {n}{\chi _{n-1,\alpha /2}^{2}}}{\hat {\sigma }}^{2}\right],$$ rather than $$\sigma ^{2}\in \left[{\frac {n-1}{\chi _{n-1,1-\alpha /2}^{2}}}s^{2},\,{\frac {n-1}{\chi _{n-1,\alpha /2}^{2}}}s^{2}\right],$$ Sparsecoder (talk) 15:49, 29 August 2024 (UTC)