Gumbel

Gumbel distribution constructor.

Usage

var Gumbel = require( '@stdlib/math/base/dists/gumbel/ctor' );

Gumbel( [mu, beta] )

Returns a Gumbel distribution object.

var gumbel = new Gumbel();

var mean = gumbel.mean;
// returns ~0.577

By default, mu = 0.0 and beta = 1.0. To create a distribution having a different mu (location parameter) and beta (scale parameter), provide parameter values.

var gumbel = new Gumbel( 2.0, 4.0 );

var mean = gumbel.mean;
// returns ~4.309

gumbel

A Gumbel distribution object has the following properties and methods...

Writable Properties

gumbel.mu

Location parameter of the distribution.

var gumbel = new Gumbel();

var mu = gumbel.mu;
// returns 0.0

gumbel.mu = 3.0;

mu = gumbel.mu;
// returns 3.0

gumbel.beta

Scale parameter of the distribution. beta must be a positive number.

var gumbel = new Gumbel( 2.0, 4.0 );

var beta = gumbel.beta;
// returns 4.0

gumbel.beta = 3.0;

beta = gumbel.beta;
// returns 3.0

Computed Properties

Gumbel.prototype.entropy

Returns the differential entropy.

var gumbel = new Gumbel( 4.0, 12.0 );

var entropy = gumbel.entropy;
// returns ~4.062

Gumbel.prototype.kurtosis

Returns the excess kurtosis.

var gumbel = new Gumbel( 4.0, 12.0 );

var kurtosis = gumbel.kurtosis;
// returns 2.4

Gumbel.prototype.mean

Returns the expected value.

var gumbel = new Gumbel( 4.0, 12.0 );

var mu = gumbel.mean;
// returns ~10.927

Gumbel.prototype.median

Returns the median.

var gumbel = new Gumbel( 4.0, 12.0 );

var median = gumbel.median;
// returns ~8.398

Gumbel.prototype.mode

Returns the mode.

var gumbel = new Gumbel( 4.0, 12.0 );

var mode = gumbel.mode;
// returns 4.0

Gumbel.prototype.skewness

Returns the skewness.

var gumbel = new Gumbel( 4.0, 12.0 );

var skewness = gumbel.skewness;
// returns ~1.14

Gumbel.prototype.stdev

Returns the standard deviation.

var gumbel = new Gumbel( 4.0, 12.0 );

var s = gumbel.stdev;
// returns ~15.391

Gumbel.prototype.variance

Returns the variance.

var gumbel = new Gumbel( 4.0, 12.0 );

var s2 = gumbel.variance;
// returns ~236.871

Methods

Gumbel.prototype.cdf( x )

Evaluates the cumulative distribution function (CDF).

var gumbel = new Gumbel( 2.0, 4.0 );

var y = gumbel.cdf( 0.5 );
// returns ~0.233

Gumbel.prototype.logcdf( x )

Evaluates the natural logarithm of the cumulative distribution function (CDF).

var gumbel = new Gumbel( 2.0, 4.0 );

var y = gumbel.logcdf( 2.0 );
// returns -1.0

Gumbel.prototype.logpdf( x )

Evaluates the natural logarithm of the probability density function (PDF).

var gumbel = new Gumbel( 2.0, 4.0 );

var y = gumbel.logpdf( 0.8 );
// returns ~-2.436

Gumbel.prototype.mgf( t )

Evaluates the moment-generating function (MGF).

var gumbel = new Gumbel( 2.0, 4.0 );

var y = gumbel.mgf( 0.1 );
// returns ~1.819

Gumbel.prototype.pdf( x )

Evaluates the probability density function (PDF).

var gumbel = new Gumbel( 2.0, 4.0 );

var y = gumbel.pdf( 2.0 );
// returns ~0.092

Gumbel.prototype.quantile( p )

Evaluates the quantile function at probability p.

var gumbel = new Gumbel( 2.0, 4.0 );

var y = gumbel.quantile( 0.5 );
// returns ~3.466

y = quantile( 1.9 );
// returns NaN

Examples

var Gumbel = require( '@stdlib/math/base/dists/gumbel/ctor' );

var gumbel = new Gumbel( 2.0, 4.0 );

var mean = gumbel.mean;
// returns ~4.309

var median = gumbel.median;
// returns ~3.466

var s2 = gumbel.variance;
// returns ~26.319

var y = gumbel.cdf( 0.8 );
// returns ~0.259