# Statistics::Distributions - phpMan

## 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)].