--- name: "PDL::Stats::Distr" section: "3pm" platform: "linux" package: "libpdl-stats-perl" version: "0.82-3" release: "Debian 12 (Bookworm)" platforms: ["linux"] url: "https://new.carta.tech/PDL::Stats::Distr" --- # PDL::Stats::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 $data = grandom(100)->abs; my ($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 \, 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.