Inverse Gamma

Inverse gamma distribution constructor.

Usage

var InvGamma = require( '@stdlib/math/base/dists/invgamma/ctor' );

InvGamma( [alpha, beta] )

Returns an inverse gamma distribution object.

var invgamma = new InvGamma();

var mode = invgamma.mode;
// returns 0.5

By default, alpha = 1.0 and beta = 1.0. To create a distribution having a different alpha (shape parameter) and beta (rate parameter), provide parameter values.

var invgamma = new InvGamma( 2.0, 4.0 );

var mu = invgamma.mean;
// returns 4.0

invgamma

An inverse gamma distribution object has the following properties and methods...

Writable Properties

invgamma.alpha

Shape parameter of the distribution. alpha must be a positive number.

var invgamma = new InvGamma();

var alpha = invgamma.alpha;
// returns 1.0

invgamma.alpha = 3.0;

alpha = invgamma.alpha;
// returns 3.0

invgamma.beta

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

var invgamma = new InvGamma( 2.0, 4.0 );

var b = invgamma.beta;
// returns 4.0

invgamma.beta = 3.0;

b = invgamma.beta;
// returns 3.0

Computed Properties

InvGamma.prototype.kurtosis

Returns the excess kurtosis.

var invgamma = new InvGamma( 6.0, 12.0 );

var kurtosis = invgamma.kurtosis;
// returns 19.0

InvGamma.prototype.mean

Returns the expected value.

var invgamma = new InvGamma( 4.0, 12.0 );

var mu = invgamma.mean;
// returns 4.0

InvGamma.prototype.mode

Returns the mode.

var invgamma = new InvGamma( 4.0, 12.0 );

var mode = invgamma.mode;
// returns 2.4

InvGamma.prototype.skewness

Returns the skewness.

var invgamma = new InvGamma( 4.0, 12.0 );

var skewness = invgamma.skewness;
// returns ~5.657

InvGamma.prototype.stdev

Returns the standard deviation.

var invgamma = new InvGamma( 4.0, 12.0 );

var s = invgamma.stdev;
// returns ~2.828

InvGamma.prototype.variance

Returns the variance.

var invgamma = new InvGamma( 4.0, 12.0 );

var s2 = invgamma.variance;
// returns 8.0

Methods

InvGamma.prototype.cdf( x )

Evaluates the cumulative distribution function (CDF).

var invgamma = new InvGamma( 2.0, 4.0 );

var y = invgamma.cdf( 0.5 );
// returns ~0.003

InvGamma.prototype.logpdf( x )

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

var invgamma = new InvGamma( 2.0, 4.0 );

var y = invgamma.logpdf( 0.8 );
// returns ~-1.556

InvGamma.prototype.pdf( x )

Evaluates the probability density function (PDF).

var invgamma = new InvGamma( 2.0, 4.0 );

var y = invgamma.pdf( 0.8 );
// returns ~0.211

InvGamma.prototype.quantile( p )

Evaluates the quantile function at probability p.

var invgamma = new InvGamma( 2.0, 4.0 );

var y = invgamma.quantile( 0.5 );
// returns ~2.383

y = quantile( 1.9 );
// returns NaN

Examples

var InvGamma = require( '@stdlib/math/base/dists/invgamma/ctor' );

var invgamma = new InvGamma( 3.0, 4.0 );

var mu = invgamma.mean;
// returns 2.0

var mode = invgamma.mode;
// returns 1.0

var s2 = invgamma.variance;
// returns 4.0

var y = invgamma.cdf( 0.8 );
// returns ~0.125