Chi

Chi distribution constructor.

Usage

var Chi = require( '@stdlib/math/base/dists/chi/ctor' );

Chi( [k] )

Returns an chi distribution object.

var chi = new Chi();

var mu = chi.mean;
// returns ~0.798

By default, k = 1.0. To create a distribution having a different degrees of freedom k, provide a parameter value.

var chi = new Chi( 4.0 );

var mu = chi.mean;
// returns ~1.88

chi

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

Writable Properties

chi.k

Degrees of freedom of the distribution. k must be a positive number.

var chi = new Chi( 2.0 );

var k = chi.k;
// returns 2.0

chi.k = 3.0;

k = chi.k;
// returns 3.0

Computed Properties

Chi.prototype.entropy

Returns the differential entropy.

var chi = new Chi( 4.0 );

var entropy = chi.entropy;
// returns ~1.019

Chi.prototype.kurtosis

Returns the excess kurtosis.

var chi = new Chi( 4.0 );

var kurtosis = chi.kurtosis;
// returns ~0.059

Chi.prototype.mean

Returns the expected value.

var chi = new Chi( 4.0 );

var mu = chi.mean;
// returns ~1.88

Chi.prototype.mode

Returns the mode.

var chi = new Chi( 4.0 );

var mode = chi.mode;
// returns ~1.732

Chi.prototype.skewness

Returns the skewness.

var chi = new Chi( 4.0 );

var skewness = chi.skewness;
// returns ~0.406

Chi.prototype.stdev

Returns the standard deviation.

var chi = new Chi( 4.0 );

var s = chi.stdev;
// returns ~0.683

Chi.prototype.variance

Returns the variance.

var chi = new Chi( 4.0 );

var s2 = chi.variance;
// returns ~0.466

Methods

Chi.prototype.cdf( x )

Evaluates the cumulative distribution function (CDF).

var chi = new Chi( 2.0 );

var y = chi.cdf( 0.5 );
// returns ~0.118

Chi.prototype.logpdf( x )

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

var chi = new Chi( 2.0 );

var y = chi.logpdf( 0.8 );
// returns ~-0.543

Chi.prototype.pdf( x )

Evaluates the probability density function (PDF).

var chi = new Chi( 2.0 );

var y = chi.pdf( 0.8 );
// returns ~0.581

Chi.prototype.quantile( p )

Evaluates the quantile function at probability p.

var chi = new Chi( 2.0 );

var y = chi.quantile( 0.5 );
// returns ~1.178

y = quantile( 1.9 );
// returns NaN

Examples

var Chi = require( '@stdlib/math/base/dists/chi/ctor' );

var chi = new Chi( 2.0 );

var mu = chi.mean;
// returns 1.253

var mode = chi.mode;
// returns 1.0

var s2 = chi.variance;
// returns ~0.429

var y = chi.cdf( 0.8 );
// returns ~0.274