A Distribution of Range of Samples taken from N(0,1)

[uart]

TL;DR Summary

Is there a name for the probability distribution of the range of a sample (size n) taken from a standard normal population?

I recently came across a distribution called the "Studentized Range" (for example, implemented as ptukey(x,n,dof) and qtukey(x,n,dof) in the R software package). Essentially it's the distribution of the range (max sample value - min sample value), for a sample (size n) taken from a student_t distribution (degrees of freedom dof).

Was just curious if there is a named distribution for the same thing except with the sample being taken from N(0,1) instead of student_t. Basically I was wondering if it's a distribution that's already implemented in various stats packages of if it just remains unnamed and unloved?

I know it can be approximated by just using a large dof in existing "Studentized Range" implementations like ptukey(), but wondering if it already exists as a named and tabulated distribution in it's own right.

 

[uart]

Just updating this thread. As far as I call tell this distribution is not commonly named or tabulated. It can however be computed from the following equation, which is a general expression for the distribution of the range (W) of a sample of random variables with distribution,density F(x),f(x).

$$F_W(W) = n \int_{-\infty}^\infty f(u) [F(u+W) - F(u)]^{n-1} du$$

I have now implemented this (crudely) in gnu Octave and it gives very good agreement with the asymptotic behavior (for large dof) of the ptukey/qtukey functions mentioned above. Can post the .m files if anyone is interested, but be warned the implementation is extremely crude and inefficient, as it was just to test that the method worked.

Reference: https://demonstrations.wolfram.com/DistributionOfTheSampleRangeOfContinuousRandomVariables/