PDL::Stats::Distr

NAME
DESCRIPTION
SYNOPSIS
FUNCTIONS
DEPENDENCIES
SEE ALSO

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: (x(); l(); float+ [o]p())
```
Probability mass function for poisson distribution. Uses Stirling's formula for x > 85.

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.
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 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_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

PDL-Stats statistics modules in Perl Data Language

PDL::Stats::Distr