Provided by: libpdl-stats-perl_0.82-3_amd64 
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 $data = grandom(100)->abs;
my ($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) = $data->mme_beta();
beta distribution. pdf: f(x; a,b) = 1/B(a,b) x^(a-1) (1-x)^(b-1)
mme_beta processes bad values. It will set the bad-value flag of all output ndarrays if
the flag is set for any of the input ndarrays.
pdf_beta
Signature: (x(); a(); b(); float+ [o]p())
probability density function for beta distribution. x defined on [0,1].
pdf_beta processes bad values. It will set the bad-value flag of all output ndarrays if
the flag is set for any of the input ndarrays.
mme_binomial
Signature: (a(n); int [o]n_(); float+ [o]p())
my ($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 processes bad values. It will set the bad-value flag of all output ndarrays
if the flag is set for any of the input ndarrays.
pmf_binomial
Signature: (ushort x(); ushort n(); p(); float+ [o]out())
probability mass function for binomial distribution.
pmf_binomial processes bad values. It will set the bad-value flag of all output ndarrays
if the flag is set for any of the input ndarrays.
mle_exp
Signature: (a(n); float+ [o]l())
my $lamda = $data->mle_exp;
exponential distribution. mle same as method of moments estimate.
mle_exp processes bad values. It will set the bad-value flag of all output ndarrays if
the flag is set for any of the input ndarrays.
pdf_exp
Signature: (x(); l(); float+ [o]p())
probability density function for exponential distribution.
pdf_exp processes bad values. It will set the bad-value flag of all output ndarrays if
the flag is set for any of the input ndarrays.
mme_gamma
Signature: (a(n); float+ [o]shape(); float+ [o]scale())
my ($shape, $scale) = $data->mme_gamma();
two-parameter gamma distribution
mme_gamma processes bad values. It will set the bad-value flag of all output ndarrays if
the flag is set for any of the input ndarrays.
pdf_gamma
Signature: (x(); a(); t(); float+ [o]p())
probability density function for two-parameter gamma distribution.
pdf_gamma processes bad values. It will set the bad-value flag of all output ndarrays if
the flag is set for any of the input ndarrays.
mle_gaussian
Signature: (a(n); float+ [o]m(); float+ [o]v())
my ($m, $v) = $data->mle_gaussian();
gaussian aka normal distribution. same results as $data->average and $data->var. mle same
as method of moments estimate.
mle_gaussian processes bad values. It will set the bad-value flag of all output ndarrays
if the flag is set for any of the input ndarrays.
pdf_gaussian
Signature: (x(); m(); v(); float+ [o]p())
probability density function for gaussian distribution.
pdf_gaussian processes bad values. It will set the bad-value flag of all output ndarrays
if the flag is set for any of the input ndarrays.
mle_geo
Signature: (a(n); float+ [o]p())
geometric distribution. mle same as method of moments estimate.
mle_geo processes bad values. It will set the bad-value flag of all output ndarrays if
the flag is set for any of the input ndarrays.
pmf_geo
Signature: (ushort x(); p(); float+ [o]out())
probability mass function for geometric distribution. x >= 0.
pmf_geo processes bad values. It will set the bad-value flag of all output ndarrays if
the flag is set for any of the input ndarrays.
mle_geosh
Signature: (a(n); float+ [o]p())
shifted geometric distribution. mle same as method of moments estimate.
mle_geosh processes bad values. It will set the bad-value flag of all output ndarrays if
the flag is set for any of the input ndarrays.
pmf_geosh
Signature: (ushort x(); p(); float+ [o]out())
probability mass function for shifted geometric distribution. x >= 1.
pmf_geosh processes bad values. It will set the bad-value flag of all output ndarrays if
the flag is set for any of the input ndarrays.
mle_lognormal
Signature: (a(n); float+ [o]m(); float+ [o]v())
my ($m, $v) = $data->mle_lognormal();
lognormal distribution. maximum likelihood estimation.
mle_lognormal processes bad values. It will set the bad-value flag of all output ndarrays
if the flag is set for any of the input ndarrays.
mme_lognormal
Signature: (a(n); float+ [o]m(); float+ [o]v())
my ($m, $v) = $data->mme_lognormal();
lognormal distribution. method of moments estimation.
mme_lognormal processes bad values. It will set the bad-value flag of all output ndarrays
if the flag is set for any of the input ndarrays.
pdf_lognormal
Signature: (x(); m(); v(); float+ [o]p())
probability density function for lognormal distribution. x > 0. v > 0.
pdf_lognormal processes bad values. It will set the bad-value flag of all output ndarrays
if the flag is set for any of the input ndarrays.
mme_nbd
Signature: (a(n); float+ [o]r(); float+ [o]p())
my ($r, $p) = $data->mme_nbd();
negative binomial distribution. pmf: f(x; r,p) = (x+r-1 r-1) p^r (1-p)^x for x=0,1,2...
mme_nbd processes bad values. It will set the bad-value flag of all output ndarrays if
the flag is set for any of the input ndarrays.
pmf_nbd
Signature: (ushort x(); r(); p(); float+ [o]out())
probability mass function for negative binomial distribution.
pmf_nbd processes bad values. It will set the bad-value flag of all output ndarrays if
the flag is set for any of the input ndarrays.
mme_pareto
Signature: (a(n); float+ [o]k(); float+ [o]xm())
my ($k, $xm) = $data->mme_pareto();
pareto distribution. pdf: f(x; k,xm) = k xm^k / x^(k+1) for x >= xm > 0.
mme_pareto processes bad values. It will set the bad-value flag of all output ndarrays if
the flag is set for any of the input ndarrays.
pdf_pareto
Signature: (x(); k(); xm(); float+ [o]p())
probability density function for pareto distribution. x >= xm > 0.
pdf_pareto processes bad values. It will set the bad-value flag of all output ndarrays if
the flag is set for any of the input ndarrays.
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 processes bad values. It will set the bad-value flag of all output ndarrays
if the flag is set for any of the input ndarrays.
pmf_poisson
Signature: (x(); l(); float+ [o]p())
Probability mass function for poisson distribution. Uses Stirling's formula for x > 85.
pmf_poisson processes bad values. It will set the bad-value flag of all output ndarrays
if the flag is set for any of the input ndarrays.
pmf_poisson_stirling
Signature: (x(); l(); [o]p())
Probability mass function for poisson distribution. Uses Stirling's formula for all values
of the input. See http://en.wikipedia.org/wiki/Stirling's_approximation for more info.
pmf_poisson_stirling processes bad values. It will set the bad-value flag of all output
ndarrays if the flag is set for any of the input ndarrays.
pmf_poisson_factorial
Signature: ushort x(); l(); float+ [o]p()
Probability mass function for poisson distribution. Input is limited to x < 170 to avoid
gsl_sf_fact() overflow.
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)
= $data->plot_distr( 'gaussian', 'lognormal', {DEV=>'/png'} );
# pars are from normalized data (ie data / bin_size)
print "$_\t@{$pars->{$_}}\n" for (sort keys %$pars);
print "$_\t$ll->{$_}\n" 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>, David Mertens
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.