Sample Range of Normal Distribution

MikeCrowe · August 29th, 2007, 9:47 am

I've definately seen something on this a long time ago but I can't remember enough about it to search for it, so if anyone can point me in the right direction that would be great.Basically I'm looking for the pdf or cdf for the sample range of a normal distribution - i.e. With sample size n, what is the pdf of the range.Anyone?

Alan · August 29th, 2007, 5:56 pm

If there are N drawings from a distribution (normal or not), the sample average x N is a random walk of N IID steps.So, you need the (large) literature on the range of a random walk, which is closely related to the range ofa (drifting) Brownian motion.See: http://cisdm.som.umass.edu/research/pdf ... ngevol.pdf, (esp. the Feller reference) in that,and Spitzer's book "Principles of Random Walk" for starters.regards,

ZmeiGorynych · August 30th, 2007, 11:37 am

this looks like it has the formula you're looking for on its first page.

MikeCrowe · September 3rd, 2007, 9:30 am

Alan:- I don't see the random walk connection to the range? I'm wanting the range of a random sample - nothing to do with any means?Zmei: - Thanks that looks like the sort of thing I remember, I knew it was messy!

Alan · September 3rd, 2007, 1:54 pm

Yeah, ignore my comments -- I misinterpretted what you were looking for.

tankt90 · September 9th, 2007, 12:58 pm

You can easily get the density functions of the min and max (they are the order statistics) of the samples. Distribution functions of range (max-min) can be calculated from random variable transformation.