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 processes 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 processes 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 processes 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 processes 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 processes 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 processes 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 processes 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 processes 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 processes 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 processes 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 processes 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 processes 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 processes 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 processes 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 processes 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 processes 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 processes 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 processes 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 processes 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 processes 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 processes 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 processes 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: (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 piddles if the flag is set for any of the input piddles.

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 piddles if the flag is set for any of the input piddles.

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

AUTHOR

To install PDL::Stats, copy and paste the appropriate command in to your terminal.

cpanm

cpanm PDL::Stats

CPAN shell

perl -MCPAN -e shell
install PDL::Stats

For more information on module installation, please visit the detailed CPAN module installation guide.

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