I've been assisting a statistical analysis project for the past couple of days. It's a multivariate problem (four for now, but possibly increasing in the near future), with about 100 observations. Since the number of variables are fixed, I've been using cubic spline interpolation for Beta and F distributions, which is close, but not exact.
We started looking for algorithms today. Being familiar with gaussian distributions in approximate molecular oribital theory, I thought to myself, "this should be a piece of cake compared to molecular orbital calculations". I was wrong! I found a pretty decent article at SpringerLink which I think will help: On the computation of the noncentral F and noncentral Beta distribution. SwRI's library has an account at SpringerLink and can obtain a copy of the article for me. I have really come up short for methods to calculate the F distribution. I am hoping this article will help. (With the caveat that I don't have a clue if I can use noncentral versions of the functions.) I also found this link to BETA_NC, which might help with the Beta calculation.
Fortunately, the premlinary work is going well and demonstrating positive results. However, I am going to need to generalize the solution to handle 'p' number of variables and 'n' number of observations for determining baselines and corresponding T2 for all observations. As α, p and n vary, I'd prefer a deterministic solution for F and Beta, as interpolating large tables can get messy very quickly.
It's rainy here in Oklahoma, and quite cool for this time of the year. Very odd.
My daughter is not happy that I made her come home and study. She wanted to go out to eat with a friend. New driver's license freedom and all that stuff...
It looks like the remnants of Ike will rain all over our parade next week, and then some.
I managed a twenty minute work out tonight. My back feels better after situps and leg lifts. My stomach does not.
I am excited over this reference to c++ statistical code I happened across this evening: C++ Source Codes. Thank you John Burkardt for publishing these algorithms..