Maggie J. Xiong > PDL-Stats-0.6.5 > PDL::Stats::Distr

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# 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' );`
`    my (\$a, \$b) = \$data->mme_beta();`

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

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

`    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

probability mass function for binomial distribution.

`    my \$lamda = \$data->mle_exp;`

exponential distribution. mle same as method of moments estimate.

probability density function for exponential distribution.

`    my (\$shape, \$scale) = \$data->mme_gamma();`

two-parameter gamma distribution

probability density function for two-parameter gamma distribution.

`    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.

probability density function for gaussian distribution.

geometric distribution. mle same as method of moments estimate.

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

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

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

`    my (\$m, \$v) = \$data->mle_lognormal();`

lognormal distribution. maximum likelihood estimation.

`    my (\$m, \$v) = \$data->mme_lognormal();`

lognormal distribution. method of moments estimation.

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

`    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...

probability mass function for negative binomial distribution.

`    my (\$k, \$xm) = \$data->mme_pareto();`

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

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

`    my \$lamda = \$data->mle_poisson();`

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

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

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_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