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

Images

Hello everybody,

I've just created an image that could replace another image in this article:

• 
  Old
• 
  New

I think the new image is better, because

• it doesn't have background
• it's a little bit easier to read
• the digits are aligned
• the SVG is valid
• the image can be created directly from the source code that is available in the description (without editing it any more)
• the $x$ looks more like an x and less like a $\chi$ (chi)

And it also has a CC0 license.

I could also re-make the other image in the same "style".

Best regards, --MartinThoma (talk) 19:38, 29 August 2014 (UTC)

@MartinThoma: It looks great! Thanks! Paul2520 (talk) 20:02, 29 August 2014 (UTC)

Characteristic function is *inverse* Fourier transform

According to the Characteristic function (probability theory) page, the CF of a distribution is the inverse Fourier transform ${\hat {\phi }}(t)=\mathbb {E} [e^{itx}]_{f(x)}$ of the PDF $f(x)$ (and therefore the frequency-domain PDF $f(x)$ is the Fourier transform of the time-domain CF ${\hat {\phi }}(t)$ ). We could just change instances of "Fourier transform" to "inverse Fourier transform", but the page goes on to say "...normal distribution on the frequency domain", so this we should also change to "...normal distribution on the time domain". I'm not missing something here, am I? Tsbertalan (talk) 23:42, 4 December 2014 (UTC)

CDF Function

The Pascal CDF function, as shown does not translate the formula shown above it. As near as I can tell, it does not provide a correct result. I suggest that for this and other examples you use a more commonly used language: C or C++. — Preceding unsigned comment added by Statguy1 (talk • contribs) 06:45, 16 February 2015 (UTC)

The Pascal code does not account for the double factorial in the denominator. This approximation of the CDF function is also given (with a reference) elsewhere in this WikiPedia article Normal_distribution#Numerical_approximations_for_the_normal_CDF — Preceding unsigned comment added by 138.73.5.2 (talk) 15:02, 22 October 2015 (UTC)

Univariate Random Variables Terminology

The top line states "This article is about the univariate normal distribution", yet the description is in terms for 'random variables', (plural) i.e. the multivariate case. I'm not sure if the plural usage 'random variables' is a formal math usage I'm not familiar with, a british/american usage difference, or just poor usage. Also, the lead paragraph does not directly state what the Normal Distribution is, but infers the definition from the CLT. I suggest restating and splitting the 2nd lead paragraph as below, and submit it to discussion here first.

-Orig The normal distribution is remarkably useful because of the central limit theorem. In its most general form, under some conditions (which include finite variance), it states that averages of random variables independently drawn from independent distributions converge in distribution to the normal, that is, become normally distributed when the number of random variables is sufficiently large. Physical quantities that are expected to be the sum of many independent processes (such as measurement errors) often have distributions that are nearly normal.[3] Moreover, many results and methods (such as propagation of uncertainty and least squares parameter fitting) can be derived analytically in explicit form when the relevant variables are normally distributed.

-Rework The normal distribution is defined by the central limit theorem. Generalized, it states, under some conditions (which include finite variance), that the distribution of averages of a random variable independently drawn from independent distributions converge to the normal distribution, when the number of samples is sufficiently large.

Physical quantities that are expected to be the sum of many independent processes (such as measurement errors) often have distributions that are nearly normal.[3] Moreover, many results and methods (such as propagation of uncertainty and least squares parameter fitting) can be derived analytically in explicit form when the relevant variables are normally distributed. LarryLACa (talk) 03:47, 13 October 2015 (UTC)

The term random variables does not commit to what type of variables we are talking about, only how many of them (more than one). There can be one univariate RV, multiple univariate RVs, one multivariate RV (i.e., a random vector), or multiple multiviarate RVs. Incidentally, in your rework, the phrase "the distribution of averages of a random variable" sounds quite awkward to my American ears. I get what you're trying to do here, but I don't think your reworked version is actually better than the original. - dcljr (talk) 22:02, 6 November 2015 (UTC)

Misuse or manipulation of the normal distribution

The applications are briefly touched on, but the danger of misapplication is completely ignored.