Talk:Studentized range distribution

Derive or explain the source of the finite df CDF equation.

For the life of me I can not figure out, nor can I find any sources for, how the CDF function arises when the degrees of freedom are finite, and k=2. It is not obvious, but the function's output DOES match table values. For the infinite df case, the derivations are obvious, replace f and F with the standard normal functions and integrate. this is not the case with finite df. Does f get replaced with t and F with T, or do we use a ratio of t and $\varphi$ to estimate S, the standard deviation?Beakerboy (talk) 14:01, 30 September 2016 (UTC)

Very strange initial sentence

This article currently begins as follows:

In probability and statistics, studentized range distribution is a continuous probability distribution that arises when estimating the range of a normally distributed population in situations where the sample size is small and population standard deviation is unknown.

What in the world is "the range of a normally distributed population"?? The normal distribution is unbounded; its "range" is infinite. That is true regardless of the the location or the scale. If what is to be estimated is a scale parameter then that is already done in computing the studentized range of the sample; it's the denominator in the studentized range. And this article doesn't even link to the studentized range article! (I'll change that.)

If the opening sentence had merely said the studentized range distribution is the probability distribution of the studentized range of an i.i.d. sample from a normally distributed population, then at least it would be comprehensible. Is that what was really intended? Or was this written by a thoroughly confused person? Michael Hardy (talk) 02:04, 2 December 2018 (UTC)

ok, Now I've changed it to read as follows:

In probability and statistics, studentized range distribution is the continuous probability distribution of the studentized range of an i.i.d. sample from a normally distributed population.

But that doesn't seem to fit well with the second paragraph. So this whole thing is still unclear. Michael Hardy (talk) 02:09, 2 December 2018 (UTC)

It looks like you have been making edits to the article for 2 years. Is this a recent realization? I agree that the opening paragraph was not great. Your version is better.Beakerboy (talk) 22:11, 3 December 2018 (UTC)

Incorrectly scaled probability density function?

The graph of the probability density function is incorrectly scaled. The "y" axis seems to be off by a factor of 1000. I'm guessing that the density was derived from the distribution by just taking the difference of consecutive points of the distribution (simple numerical differentiation), however it should then have been scaled by the reciprocal of the sampling interval (which is presumably 0.001 given the approx 1000 scale factor error). 193.82.247.240 (talk) 13:31, 21 May 2025 (UTC)