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ChiSquare

Chi-squared distribution constructor.

Installation

npm install @stdlib/stats-base-dists-chisquare-ctor

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

var ChiSquare = require( '@stdlib/stats-base-dists-chisquare-ctor' );

ChiSquare( [k] )

Returns an chi-squared distribution object.

var chisquare = new ChiSquare();

var mu = chisquare.mean;
// returns 1.0

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

var chisquare = new ChiSquare( 4.0 );

var mu = chisquare.mean;
// returns 4.0

---

chisquare

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

Writable Properties

chisquare.k

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

var chisquare = new ChiSquare( 2.0 );

var k = chisquare.k;
// returns 2.0

chisquare.k = 3.0;

k = chisquare.k;
// returns 3.0

---

Computed Properties

ChiSquare.prototype.entropy

Returns the differential entropy.

var chisquare = new ChiSquare( 4.0 );

var entropy = chisquare.entropy;
// returns ~2.27

ChiSquare.prototype.kurtosis

Returns the excess kurtosis.

var chisquare = new ChiSquare( 4.0 );

var kurtosis = chisquare.kurtosis;
// returns 3.0

ChiSquare.prototype.mean

Returns the expected value.

var chisquare = new ChiSquare( 4.0 );

var mu = chisquare.mean;
// returns 4.0

ChiSquare.prototype.median

Returns the median.

var chisquare = new ChiSquare( 4.0 );

var median = chisquare.median;
// returns ~3.357

ChiSquare.prototype.mode

Returns the mode.

var chisquare = new ChiSquare( 4.0 );

var mode = chisquare.mode;
// returns 2.0

ChiSquare.prototype.skewness

Returns the skewness.

var chisquare = new ChiSquare( 4.0 );

var skewness = chisquare.skewness;
// returns ~1.414

ChiSquare.prototype.stdev

Returns the standard deviation.

var chisquare = new ChiSquare( 4.0 );

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

ChiSquare.prototype.variance

Returns the variance.

var chisquare = new ChiSquare( 4.0 );

var s2 = chisquare.variance;
// returns 8.0

---

Methods

ChiSquare.prototype.cdf( x )

Evaluates the cumulative distribution function (CDF).

var chisquare = new ChiSquare( 2.0 );

var y = chisquare.cdf( 0.5 );
// returns ~0.221

ChiSquare.prototype.mgf( t )

Evaluates the moment-generating function (MGF).

var chisquare = new ChiSquare( 2.0 );

var y = chisquare.mgf( 0.2 );
// returns ~1.667

ChiSquare.prototype.pdf( x )

Evaluates the probability density function (PDF).

var chisquare = new ChiSquare( 2.0 );

var y = chisquare.pdf( 0.8 );
// returns ~0.335

ChiSquare.prototype.quantile( p )

Evaluates the quantile function at probability p.

var chisquare = new ChiSquare( 2.0 );

var y = chisquare.quantile( 0.5 );
// returns ~1.386

y = chisquare.quantile( 1.9 );
// returns NaN

---

Examples

var ChiSquare = require( '@stdlib/stats-base-dists-chisquare-ctor' );

var chisquare = new ChiSquare( 2.0 );

var mu = chisquare.mean;
// returns 2.0

var mode = chisquare.mode;
// returns 0.0

var s2 = chisquare.variance;
// returns 4.0

var y = chisquare.cdf( 0.8 );
// returns ~0.33

---

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.