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)