# NAME

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

# SYNOPSIS

```
use Statistics::Distributions;
$chis=Statistics::Distributions::chisqrdistr (2,.05);
print "Chi-squared-crit (2 degrees of freedom, 95th percentile "
."= 0.05 level) = $chis\n";
$u=Statistics::Distributions::udistr (.05);
print "u-crit (95th percentile = 0.05 level) = $u\n";
$t=Statistics::Distributions::tdistr (1,.005);
print "t-crit (1 degree of freedom, 99.5th percentile = 0.005 level) "
."= $t\n";
$f=Statistics::Distributions::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\n";
$uprob=Statistics::Distributions::uprob (-0.85);
print "upper probability of the u distribution (u = -0.85): Q(u) "
."= 1-G(u) = $uprob\n";
$chisprob=Statistics::Distributions::chisqrprob (3,6.25);
print "upper probability of the chi-square distribution (3 degrees "
."of freedom, chi-squared = 6.25): Q = 1-G = $chisprob\n";
$tprob=Statistics::Distributions::tprob (3,6.251);
print "upper probability of the t distribution (3 degrees of "
."freedom, t = 6.251): Q = 1-G = $tprob\n";
$fprob=Statistics::Distributions::fprob (3,5,.625);
print "upper probability of the F distribution (3 degrees of freedom "
."in numerator, 5 degrees of freedom in denominator, F = 6.25): "
."Q = 1-G = $fprob\n";
```

# DESCRIPTION

This Perl module calculates percentage points (5 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 (5 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 F test and the chi-squared 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)

# BUGS

This final version 1.02 has been released after more than one year without a bug report on the previous version 0.07. Nevertheless, if you find any bugs or oddities, please do inform the author.

# INSTALLATION

See perlmodinstall for information and options on installing Perl modules.

# AVAILABILITY

The latest version of this module is available from the Distribution Perl Archive Network (CPAN). Please visit http://www.cpan.org/ to find a CPAN site near you or see http://www.cpan.org/authors/id/M/MI/MIKEK/ .

# AUTHOR

Michael Kospach <mike.perl@gmx.at>

Nice formating, simplification and bug repair by Matthias Trautner Kromann <mtk@id.cbs.dk>

# COPYRIGHT

Copyright 2003 Michael Kospach. All rights reserved.

This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself.

# SEE ALSO

Statistics::ChiSquare, Statistics::Table::t, Statistics::Table::F, perl(1).