Chi-squared

Chi-squared distribution.

Usage

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

chisquare

Chi-squared distribution.

var dist = chisquare;
// returns {...}

The namespace contains the following distribution functions:

cdf( x, k ): Chi-squared distribution cumulative distribution function.
logpdf( x, k ): evaluate the natural logarithm of the probability density function (PDF) for a chi-squared distribution.
mgf( t, k ): Chi-squared distribution moment-generating function (MGF).
pdf( x, k ): Chi-squared distribution probability density function (PDF).
quantile( p, k ): Chi-squared distribution quantile function.

The namespace contains the following functions for calculating distribution properties:

entropy( k ): Chi-squared distribution differential entropy.
kurtosis( k ): Chi-squared distribution excess kurtosis.
mean( k ): Chi-squared distribution expected value.
median( k ): Chi-squared distribution median.
mode( k ): Chi-squared distribution mode.
skewness( k ): Chi-squared distribution skewness.
stdev( k ): Chi-squared distribution standard deviation.
variance( k ): Chi-squared distribution variance.

The namespace contains a constructor function for creating a Chi-squared distribution object.

ChiSquare( [k] ): Chi-squared distribution constructor.

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

var dist = new ChiSquare( 4.0 );

var mu = dist.mean;
// returns 4.0

Examples

var roundn = require( '@stdlib/math/base/special/roundn' );
var chisquare = require( '@stdlib/stats/base/dists/chisquare' );

// Define degrees of freedom:
var k = 5.0;

// Calculate distribution properties:
console.log( 'Mean: %d', chisquare.mean( k ) );
console.log( 'Median: %d', roundn( chisquare.median( k ), -4 ) );
console.log( 'Mode: %d', chisquare.mode( k ) );
console.log( 'Variance: %d', chisquare.variance( k ) );
console.log( 'Standard Deviation: %d', roundn( chisquare.stdev( k ), -4 ) );
console.log( 'Skewness: %d', roundn( chisquare.skewness( k ), -4 ) );
console.log( 'Excess Kurtosis: %d', roundn( chisquare.kurtosis( k ), -4 ) );
console.log( 'Entropy: %d', roundn( chisquare.entropy( k ), -4 ) );

// Evaluate probability functions:
var x = 3.0;
console.log( '\nEvaluating at x = %d', x );
console.log( 'PDF: %d', roundn( chisquare.pdf( x, k ), -4 ) );
console.log( 'logPDF: %d', roundn( chisquare.logpdf( x, k ), -4 ) );
console.log( 'CDF: %d', roundn( chisquare.cdf( x, k ), -4 ) );

// Calculate quantiles:
var p = 0.7;
console.log( '\nQuantile at p = %d: %d', p, roundn( chisquare.quantile( p, k ), -4 ) );

// Evaluate moment-generating function:
var t = 0.1;
console.log( 'MGF at t = %d: %d', t, roundn( chisquare.mgf( t, k ), -4 ) );