(35S) Statistical Distributions Functions

[Dieter]

(11-01-2015 12:44 PM)PedroLeiva Wrote:  Dieter, to contribute to your work on Statistical Distribution Functions, herewith a pdf with instructions for execution of the compiled program you are developing. I ask for corrections and comments. From already thank you very much for your effort.

Thank you – I appreciate your efforts. You did quite some work for a program that is still under development. ;-)

The instructions say that "x" is calculated for a quantile. Actually the quantile is x. The programs determine the quantile x for a given probability p. The latter is not given in % or ‰ (c.f. Student distr.). After each iteration step, Y and X show the previous resp. current approximation. This is helpful in some extreme cases where both the CDF and the quantile currently can only be calculated with limited accuracy.

The returned CDF is always the integral from –∞ to x (resp. 0 to x for Chi²), i.e. the "left side integral", which is usually called P(x). This is also true for the F distribution where HP's manual says that P(x) is the "right side integral", which usually is called Q(x). So the current F implementation returns Q(x) in Y and P(x) in X.

I know want to change the general approach in that I'd like to provide two basic routines that evaluate the reqularized incomplete Beta and Gamma function (actually four routines as both functions are evaluated either by a series expansion or continued fractions). Beta can be used to calculate the Student and Fisher distribution, and Gamma does it for the Normal and Chi² distribution. Execution times seem to be a bit longer, but on the other hand now even cases far out in the distribution tails can be handled. The plan is to get reasonably accurate results even for p=1E–499. ;-)

(11-01-2015 12:44 PM)PedroLeiva Wrote:  NOTE: it was impossible to attach an Excel file

That's easy: simply zip it.

Dieter