NAME

Statistics::Distrib::Normal - the normal distribution


SYNOPSIS

    use Statistics::Distrib::Normal;
    $dist = new Statistics::Distrib::Normal;
    $dist->mu(3);                # set the location parameter
    $dist->sigma(5);             # set the scale parameter
    @x = $dist->rand(10);        # generate random numbers
    # or
    @x = Statistics::Distrib::Normal->new(Mu => 3, Sigma => 5)->rand(10);

DESCRIPTION

This module contains miscellaneous functions related to the normal distribution.


CONSTRUCTOR

new ( [ OPTIONS ] )
OPTIONS is a list of options given in the form of key-value pairs, just like a hash table. Valid options are
Mu
Sets the mu parameter (the mean) of the distribution to the specified value.
Sigma
Sets the sigma parameter (the standard deviation) of the distribution to the specified value.

METHODS

mean ( [ MEAN ] )
Set the mu parameter (the mean) of the distribution to MU. If MU is omitted, the current value of mu is returned.
sigma ( [ SDEV ] )
Set the sigma parameter (the standard deviation) of the distribution to SIGMA. If SIGMA is omitted, the current value of sigma is returned.
pdf ( X1 [, X2 [, X3 ... ] ] )
Evaluate the probability density function at X1, X2, X3, ...
ltp ( X1 [, X2 [, ... ] ] )
Evaluate the lower tail probability function at X1, X2, X3, ...
utp ( X1 [, X2 [, ... ] ] )
Evaluate the upper tail probability function at X1, X2, X3, ...
ltq ( P1 [, P2 [, ... ] ] )
Returns the lower tail quantile for the probabilities P1, P2, P3, ...
utq ( P1 [, P2 [, P3 ... ] ] )
Returns the upper tail quantile for the probabilities P1, P2, P3, ...
intprob( XLOW, XHIGH )
Interval probability. Returns the probability of an outcome in the interval from XLOW to XHIGH.
rand( [ NUM ] )
Generate random variables. If NUM is omitted, a single variable is returned.
expectation ()
Return the expectation of the distribution.
variance ()
Return the variance of the distribution.
skewness ()
Return the skewness of the distribution.
kurtosis ()
Return the kurtosis (normalized) of the distribution.
dmo
Direct moments for the distribution.

Not implemented yet.

cmo
Central moments for the distribution.
mode ()
Returns the mode of the distribution.

BUGS

None known.


LIMITATIONS

Degenerate cases are not allowed for most methods; e.g., a distribution with zero variance.


HISTORY

Version 0.02
Code formatting changes.
Version 0.01
First release.

AUTHOR

Peter John Acklam <pjacklam@online.no>.


COPYRIGHT/LICENSE

Copyright 1999-2000 Peter John Acklam. This program is free software; you can redistribute it and/or modify it under the same terms as Perl itself.