# Statistics::Distributions - Perl module for calculating probabilities and critical values of common statistical distributions

### From WeBWorK

# NAME

Statistics::Distributions - Perl module for calculating probabilities and critical values of common statistical distributions

# SYNOPSIS

use Statistics::Distributions;

$uprob=uprob(-0.85); print "upper probability of the u distribution: Q(u) = 1-G(u) (u=1.43) = $uprob";

$tprob=tprob(3, 6.251); print "upper probability of the t distribution: Q = 1-G (3 degrees of freedom , t = 6.251) = $tprob";

$chisprob=chisqrprob(3, 6.25); print "upper probability of the chi-square distribution: Q = 1-G (3 degrees of freedom, chi-squared = 6.25) = $chisprob";

$fprob=fprob(3,5, .625); print "upper probability of the F distribution: Q = 1-G (3 degrees of freedom in numerator, 5 degrees of freedom in denominator, F $

$u=udistr(.05); print "u-crit (95th percentile = 0.05 level) = $u";

$t=tdistr(1, .005); print "t-crit (1 degree of freedom, 99.5th percentile = 0.005 level) =$t";

$chis=chisqrdistr(2, .05); print "Chi-squared-crit (2 degrees of freedom, 95th percentile = 0.05 level) = $chis";

$f=fdistr(1,3, .01); print "F-crit (1 degree of freedom in numerator, 3 degrees of freedom in denominator, 99th percentile = 0.01 level) = $f";

# DESCRIPTION

This Perl module calulates percentage points (6 significant digits) of the u (standard normal) distribution, the student's t distribution, the chi-square distribution and the F distribution.

It can also calculate the upper probability (6 significant digits) of the u (standard normal), the chi-square, the t and the F distribution.

These critical values are needed to perform statistical tests, like the u test, the t test, the chi-squared test, and the F test, and to calculate confidence intervals.

If you are interested in more precise algorithms you could look at: StatLib: http://lib.stat.cmu.edu/apstat/ Applied Statistics Algorithms by Griffiths, P. and Hill, I.D., Ellis Horwood: Chichester (1985)

# AUTHOR

Michael Kospach, mike.perl@gmx.at Nice formating, simplification and bug repair by Matthias Trautner Kromann, mtk@id.cbs.dk