Distr(3pm)						User Contributed Perl Documentation						Distr(3pm)

NAME

       PDL::Stats::Distr -- parameter estimations and probability density functions for distributions.

DESCRIPTION

       Parameter estimate is maximum likelihood estimate when there is closed form estimate, otherwise it is method of moments estimate.

SYNOPSIS

	   use PDL::LiteF;
	   use PDL::Stats::Distr;

	     # do a frequency (probability) plot with fitted normal curve

	   my ($xvals, $hist) = $data->hist;

	     # turn frequency into probability
	   $hist /= $data->nelem;

	     # get maximum likelihood estimates of normal curve parameters
	   my ($m, $v) = $data->mle_gaussian();

	     # fitted normal curve probabilities
	   my $p = $xvals->pdf_gaussian($m, $v);

	   use PDL::Graphics::PGPLOT::Window;
	   my $win = pgwin( Dev=>"/xs" );

	   $win->bin( $hist );
	   $win->hold;
	   $win->line( $p, {COLOR=>2} );
	   $win->close;

       Or, play with different distributions with plot_distr :)

	   $data->plot_distr( 'gaussian', 'lognormal' );

FUNCTIONS

   mme_beta
	 Signature: (a(n); float+ [o]alpha(); float+ [o]beta())

	   my ($a, $b) = $data->mme_beta();

       beta distribution. pdf: f(x; a,b) = 1/B(a,b) x^(a-1) (1-x)^(b-1)

       mme_beta does handle bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

   pdf_beta
	 Signature: (x(); a(); b(); float+ [o]p())

       probability density function for beta distribution. x defined on [0,1].

       pdf_beta does handle bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

   mme_binomial
	 Signature: (a(n); int [o]n_(); float+ [o]p())

	   my ($n, $p) = $data->mme_binomial;

       binomial distribution. pmf: f(k; n,p) = (n k) p^k (1-p)^(n-k) for k = 0,1,2..n

       mme_binomial does handle bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

   pmf_binomial
	 Signature: (ushort x(); ushort n(); p(); float+ [o]out())

       probability mass function for binomial distribution.

       pmf_binomial does handle bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

   mle_exp
	 Signature: (a(n); float+ [o]l())

	   my $lamda = $data->mle_exp;

       exponential distribution. mle same as method of moments estimate.

       mle_exp does handle bad values.	It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

   pdf_exp
	 Signature: (x(); l(); float+ [o]p())

       probability density function for exponential distribution.

       pdf_exp does handle bad values.	It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

   mme_gamma
	 Signature: (a(n); float+ [o]shape(); float+ [o]scale())

	   my ($shape, $scale) = $data->mme_gamma();

       two-parameter gamma distribution

       mme_gamma does handle bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

   pdf_gamma
	 Signature: (x(); a(); t(); float+ [o]p())

       probability density function for two-parameter gamma distribution.

       pdf_gamma does handle bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

   mle_gaussian
	 Signature: (a(n); float+ [o]m(); float+ [o]v())

	   my ($m, $v) = $data->mle_gaussian();

       gaussian aka normal distribution. same results as $data->average and $data->var. mle same as method of moments estimate.

       mle_gaussian does handle bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

   pdf_gaussian
	 Signature: (x(); m(); v(); float+ [o]p())

       probability density function for gaussian distribution.

       pdf_gaussian does handle bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

   mle_geo
	 Signature: (a(n); float+ [o]p())

       geometric distribution. mle same as method of moments estimate.

       mle_geo does handle bad values.	It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

   pmf_geo
	 Signature: (ushort x(); p(); float+ [o]out())

       probability mass function for geometric distribution. x >= 0.

       pmf_geo does handle bad values.	It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

   mle_geosh
	 Signature: (a(n); float+ [o]p())

       shifted geometric distribution. mle same as method of moments estimate.

       mle_geosh does handle bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

   pmf_geosh
	 Signature: (ushort x(); p(); float+ [o]out())

       probability mass function for shifted geometric distribution. x >= 1.

       pmf_geosh does handle bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

   mle_lognormal
	 Signature: (a(n); float+ [o]m(); float+ [o]v())

	   my ($m, $v) = $data->mle_lognormal();

       lognormal distribution. maximum likelihood estimation.

       mle_lognormal does handle bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input
       piddles.

   mme_lognormal
	 Signature: (a(n); float+ [o]m(); float+ [o]v())

	   my ($m, $v) = $data->mme_lognormal();

       lognormal distribution. method of moments estimation.

       mme_lognormal does handle bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input
       piddles.

   pdf_lognormal
	 Signature: (x(); m(); v(); float+ [o]p())

       probability density function for lognormal distribution. x > 0. v > 0.

       pdf_lognormal does handle bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input
       piddles.

   mme_nbd
	 Signature: (a(n); float+ [o]r(); float+ [o]p())

	   my ($r, $p) = $data->mme_nbd();

       negative binomial distribution. pmf: f(x; r,p) = (x+r-1	r-1) p^r (1-p)^x for x=0,1,2...

       mme_nbd does handle bad values.	It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

   pmf_nbd
	 Signature: (ushort x(); r(); p(); float+ [o]out())

       probability mass function for negative binomial distribution.

       pmf_nbd does handle bad values.	It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

   mme_pareto
	 Signature: (a(n); float+ [o]k(); float+ [o]xm())

	   my ($k, $xm) = $data->mme_pareto();

       pareto distribution. pdf: f(x; k,xm) = k xm^k / x^(k+1) for x >= xm > 0.

       mme_pareto does handle bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

   pdf_pareto
	 Signature: (x(); k(); xm(); float+ [o]p())

       probability density function for pareto distribution. x >= xm > 0.

       pdf_pareto does handle bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

   mle_poisson
	 Signature: (a(n); float+ [o]l())

	   my $lamda = $data->mle_poisson();

       poisson distribution. pmf: f(x;l) = e^(-l) * l^x / x!

       mle_poisson does handle bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

   pmf_poisson
	 Signature: (ushort x(); l(); float+ [o]p())

       probability mass function for poisson distribution.

       pmf_poisson does handle bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

   plot_distr
       Plots data distribution. When given specific distribution(s) to fit, returns % ref to sum log likelihood and parameter values under fitted
       distribution(s). See FUNCTIONS above for available distributions.

       Default options (case insensitive):

	   MAXBN => 20,
	     # see PDL::Graphics::PGPLOT::Window for next options
	   WIN	 => undef,   # pgwin object. not closed here if passed
			     # allows comparing multiple distr in same plot
			     # set env before passing WIN
	   DEV	 => '/xs' ,  # open and close dev for plotting if no WIN
			     # defaults to '/png' in Windows
	   COLOR => 1,	     # color for data distr

       Usage:

	     # yes it threads :)
	   my $data = grandom( 500, 3 )->abs;
	     # ll on plot is sum across 3 data curves
	   my ($ll, $pars)
	     = $data->plot_distr( 'gaussian', 'lognormal', {DEV=>'/png'} );

	     # pars are from normalized data (ie data / bin_size)
	   print "$_	@{$pars->{$_}}
" for (sort keys %$pars);
	   print "$_	$ll->{$_}
" for (sort keys %$ll);

DEPENDENCIES

       GSL - GNU Scientific Library

SEE ALSO

       PDL::Graphics::PGPLOT

       PDL::GSL::CDF

AUTHOR

       Copyright (C) 2009 Maggie J. Xiong <maggiexyz users.sourceforge.net>

       All rights reserved. There is no warranty. You are allowed to redistribute this software / documentation as described in the file COPYING
       in the PDL distribution.

perl v5.14.2							    2012-06-04								Distr(3pm)