/ 
PDL-Stats-0.2.6
River stage one • 3 direct dependents • 4 total dependents
/ PDL::Stats::Distr

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
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'} );

print "$_\t$ll->{$_}\n" for (sort keys %$ll);
print "$_\t@{$pars->{$_}}\n" for (sort keys %$pars);

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.