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PDL-GSL-2.103
River stage one • 1 direct dependent • 3 total dependents
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/ 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 $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::Simple;
my $win = pgswin();
$win->plot( with=>'bins', $hist, with=>'lines', style => 2, $p );
undef $win; # to 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())
Types: (float double ldouble)
my ($a, $b) = $data->mme_beta();

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

Broadcasts over its inputs.

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())
Types: (float double ldouble)
$p = pdf_beta($x, $a, $b);
pdf_beta($x, $a, $b, $p);  # all arguments given
$p = $x->pdf_beta($a, $b); # method call
$x->pdf_beta($a, $b, $p);

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

Broadcasts over its inputs.

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())
Types: (float double ldouble)
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

Broadcasts over its inputs.

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())
Types: (float double ldouble)
$out = pmf_binomial($x, $n, $p);
pmf_binomial($x, $n, $p, $out);  # all arguments given
$out = $x->pmf_binomial($n, $p); # method call
$x->pmf_binomial($n, $p, $out);

probability mass function for binomial distribution.

Broadcasts over its inputs.

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())
Types: (float double ldouble)
my $lamda = $data->mle_exp;

exponential distribution. mle same as method of moments estimate.

Broadcasts over its inputs.

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())
Types: (float double ldouble)
$p = pdf_exp($x, $l);
pdf_exp($x, $l, $p);  # all arguments given
$p = $x->pdf_exp($l); # method call
$x->pdf_exp($l, $p);

probability density function for exponential distribution.

Broadcasts over its inputs.

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())
Types: (float double ldouble)
my ($shape, $scale) = $data->mme_gamma();

two-parameter gamma distribution

Broadcasts over its inputs.

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())
Types: (float double ldouble)
$p = pdf_gamma($x, $a, $t);
pdf_gamma($x, $a, $t, $p);  # all arguments given
$p = $x->pdf_gamma($a, $t); # method call
$x->pdf_gamma($a, $t, $p);

probability density function for two-parameter gamma distribution.

Broadcasts over its inputs.

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())
Types: (float double ldouble)
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.

Broadcasts over its inputs.

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())
Types: (float double ldouble)
$p = pdf_gaussian($x, $m, $v);
pdf_gaussian($x, $m, $v, $p);  # all arguments given
$p = $x->pdf_gaussian($m, $v); # method call
$x->pdf_gaussian($m, $v, $p);

probability density function for gaussian distribution.

Broadcasts over its inputs.

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())
Types: (float double ldouble)
$p = mle_geo($a);
mle_geo($a, $p);  # all arguments given
$p = $a->mle_geo; # method call
$a->mle_geo($p);

geometric distribution. mle same as method of moments estimate.

Broadcasts over its inputs.

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())
Types: (float double ldouble)
$out = pmf_geo($x, $p);
pmf_geo($x, $p, $out);  # all arguments given
$out = $x->pmf_geo($p); # method call
$x->pmf_geo($p, $out);

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

Broadcasts over its inputs.

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())
Types: (float double ldouble)
$p = mle_geosh($a);
mle_geosh($a, $p);  # all arguments given
$p = $a->mle_geosh; # method call
$a->mle_geosh($p);

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

Broadcasts over its inputs.

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())
Types: (float double ldouble)
$out = pmf_geosh($x, $p);
pmf_geosh($x, $p, $out);  # all arguments given
$out = $x->pmf_geosh($p); # method call
$x->pmf_geosh($p, $out);

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

Broadcasts over its inputs.

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())
Types: (float double ldouble)
my ($m, $v) = $data->mle_lognormal();

lognormal distribution. maximum likelihood estimation.

Broadcasts over its inputs.

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())
Types: (float double ldouble)
my ($m, $v) = $data->mme_lognormal();

lognormal distribution. method of moments estimation.

Broadcasts over its inputs.

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())
Types: (float double ldouble)
$p = pdf_lognormal($x, $m, $v);
pdf_lognormal($x, $m, $v, $p);  # all arguments given
$p = $x->pdf_lognormal($m, $v); # method call
$x->pdf_lognormal($m, $v, $p);

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

Broadcasts over its inputs.

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())
Types: (float double ldouble)
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...

Broadcasts over its inputs.

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())
Types: (float double ldouble)
$out = pmf_nbd($x, $r, $p);
pmf_nbd($x, $r, $p, $out);  # all arguments given
$out = $x->pmf_nbd($r, $p); # method call
$x->pmf_nbd($r, $p, $out);

probability mass function for negative binomial distribution.

Broadcasts over its inputs.

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())
Types: (float double ldouble)
my ($k, $xm) = $data->mme_pareto();

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

Broadcasts over its inputs.

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())
Types: (float double ldouble)
$p = pdf_pareto($x, $k, $xm);
pdf_pareto($x, $k, $xm, $p);  # all arguments given
$p = $x->pdf_pareto($k, $xm); # method call
$x->pdf_pareto($k, $xm, $p);

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

Broadcasts over its inputs.

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())
Types: (float double ldouble)
my $lamda = $data->mle_poisson();

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

Broadcasts over its inputs.

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())
Types: (float double ldouble)
$p = pmf_poisson($x, $l);
pmf_poisson($x, $l, $p);  # all arguments given
$p = $x->pmf_poisson($l); # method call
$x->pmf_poisson($l, $p);

Probability mass function for poisson distribution. Uses Stirling's formula for x > 85.

Broadcasts over its inputs.

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())
Types: (float double ldouble)
$p = pmf_poisson_stirling($x, $l);
pmf_poisson_stirling($x, $l, $p);  # all arguments given
$p = $x->pmf_poisson_stirling($l); # method call
$x->pmf_poisson_stirling($l, $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.

Broadcasts over its inputs.

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())
Types: (float double ldouble)
$p = pmf_poisson_factorial($x, $l);
pmf_poisson_factorial($x, $l, $p);  # all arguments given
$p = $x->pmf_poisson_factorial($l); # method call
$x->pmf_poisson_factorial($l, $p);

Probability mass function for poisson distribution. Input is limited to x < 170 to avoid gsl_sf_fact() overflow.

Broadcasts over its inputs.

pmf_poisson_factorial 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.

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::Simple for next options
WIN   => undef,   # pgswin object. not closed here if passed
                  # allows comparing multiple distr in same plot
                  # set env before passing WIN
COLOR => 1,       # "style" 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' );

  # 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::Simple

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.