Computing Statistical Distributions: A Practical Guide

[Hurkyl]

How does one go about actually computing various statistical tables, rather than looking them up?

Things of interest at the moment are the cumulative distributions and their inverses, for the standard normal and both central and noncentral chi squares.

 

[PerennialII]

I typically resort to curve fitting (regression analysis) rather than using the tables overall, basic (nonlinear) least squares and maximum likelihood methods for one work pretty well for most common distributions.

 

[Hurkyl]

I don't know if I can use that for my purposes... one of the particular questions I'd like to answer is how many data points I need for the false positive rate of my test to be less than 2^-20. (And I might be being conservative on just how small I want the rate)

Actually... now that I think about it, I might be outside the domain where the normal approximation is reasonable for my simpler test. (or a nonlinear Chi square approximation for the more complicated test) Blech.

Anyways, the simpler test was testing a sample mean for being nonzero, when the statistic is approximately normally distributed with variance 1. The more complicated one was the same spirit, except I was summing squares of many of these statistics.

 

[juvenal]

How does one go about actually computing various statistical tables, rather than looking them up?

Things of interest at the moment are the cumulative distributions and their inverses, for the standard normal and both central and noncentral chi squares.

Do you have access to Mathematica? That's what I'd use.