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)

I have endeavored to add some text to the lead (supported by citations to college study materials) that will be intelligible to the layman. My work here is finished, but there's more that needs to be done - all those equations, or at least some of them, need to be supported with citations to reliable sources. I'm not enough of a mathematician to take that on, so I hope someone else will step in. Meliora! BuzzWeiser196 (talk) 20:23, 17 November 2024 (UTC)

While I appreciate the effort, a lot of critical information has been stripped from the intro (like its definition, the fact that it's a probability distribution, any mention of random variables, and its relation to the central limit theorem). The intro text is now overly specific to a few applications (the mentions of IQ and real estate prices in the first paragraph are unnecessary) and it ignores the distribution's fundamental importance to science. I think it would be better to revert to the previous text and point out parts that you find confusing so we can help fix it. Citing (talk) 20:02, 22 November 2024 (UTC)

Citing (talk): Re: The Normal Distribution article, I guess this is a case of which audience the lead is aimed at. You've written the lead for a specialist. I was trying to write a lead for the layman, with simple terms the average reader can understand. That makes it easier for the reader to decide whether he wants to read further. Of course "continuous probability distribution", "valued random interval", "probability density function" and the equation all belong in article. But they just get in the way when we're trying to give the reader a quick take. I also noted that most of the many equations lack inline citations to reliable sources. I'm going to step away from this article now. I don't relish conflict. Go forth and do great work! Cordially, BuzzWeiser196 (talk) 15:47, 23 November 2024 (UTC)

@Willondon: Responding to your comment "There are citations aplenty" accompanying my last edit to this article: I must disagree. The first equation in the article ought to have an inline citation to a reliable source. If it came from a textbook, tell us who authored that textbook and on which page it can be found. I have the same concern about many of the equations that appear later in the article. Cordially, BuzzWeiser196 (talk) 22:27, 29 December 2024 (UTC)

I restored the tag. I was responding to the sheer volume of citations in the article, of which there are plenty. I see now from your comments, that doesn't mean the list is thorough or complete. _signed, Willondon (talk) 15:55, 30 December 2024 (UTC)

@Willondon : Thanks for reconsidering. My best to you! BuzzWeiser196 (talk) 16:17, 30 December 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)

these are often denoting different estimators.

S is often based on dividing by n-1 (unbiased estimator, but also, more importantly, the estimator that is needed for t distribution to emerge).

While sigma hat is based on doviding by n (mle estimator). Tal Galili (talk) 20:31, 29 November 2024 (UTC)