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Cumulative Distribution Function

Chi distribution cumulative distribution function.

The cumulative distribution function for a chi random variable is

$$F(x;\,k) = P\left(k/2,x^{2}/2\right)$$

where k is the degrees of freedom and P is the lower regularized incomplete gamma function.

Usage

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

cdf( x, k )

Evaluates the cumulative distribution function (CDF) for a chi distribution with degrees of freedom k.

var y = cdf( 2.0, 1.0 );
// returns ~0.954

y = cdf( 2.0, 3.0 );
// returns ~0.739

y = cdf( 1.0, 0.5 );
// returns ~0.846

y = cdf( -1.0, 2.0 );
// returns 0.0

y = cdf( -Infinity, 4.0 );
// returns 0.0

y = cdf( +Infinity, 4.0 );
// returns 1.0

If provided NaN as any argument, the function returns NaN.

var y = cdf( NaN, 1.0 );
// returns NaN

y = cdf( 0.0, NaN );
// returns NaN

If provided k < 0, the function returns NaN.

var y = cdf( 2.0, -2.0 );
// returns NaN

If provided k = 0, the function evaluates the CDF of a degenerate distribution centered at 0.

var y = cdf( 2.0, 0.0 );
// returns 1.0

y = cdf( -2.0, 0.0 );
// returns 0.0

y = cdf( 0.0, 0.0 );
// returns 1.0

cdf.factory( k )

Returns a function for evaluating the cumulative distribution function for a chi distribution with degrees of freedom k.

var mycdf = cdf.factory( 3.0 );

var y = mycdf( 6.0 );
// returns ~1.0

y = mycdf( 1.5 );
// returns ~0.478

Examples

var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var uniform = require( '@stdlib/random/array/uniform' );
var logEachMap = require( '@stdlib/console/log-each-map' );
var cdf = require( '@stdlib/stats/base/dists/chi/cdf' );

var opts = {
    'dtype': 'float64'
};
var x = uniform( 20, 0.0, 10.0, opts );
var k = discreteUniform( 20, 0, 10, opts );

logEachMap( 'x: %0.4f, k: %d, F(x;k): %0.4f', x, k, cdf );

C APIs

Usage

#include "stdlib/stats/base/dists/chi/cdf.h"

stdlib_base_dists_chi_cdf( x, k )

Evaluates the cumulative distribution function (CDF) for a chi distribution with degrees of freedom k.

double out = stdlib_base_dists_chi_cdf( 2.0, 1.0 );
// returns ~0.954

out = stdlib_base_dists_chi_cdf( 2.0, 3.0 );
// returns ~0.739

The function accepts the following arguments:

  • x: [in] double input value.
  • k: [in] double degrees of freedom.
double stdlib_base_dists_chi_cdf( const double x, const double k );

Examples

#include "stdlib/stats/base/dists/chi/cdf.h"
#include <stdlib.h>
#include <stdio.h>

static double random_uniform( double a, double b ) {
    double r = ( (double)rand() / ( (double)RAND_MAX + 1.0 ) );
    return a + ( r * ( b - a ) );
}

int main( void ) {
    double x;
    double k;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        x = random_uniform( 0.0, 2.0 );
        k = random_uniform( 1.0, 10.0 );
        y = stdlib_base_dists_chi_cdf( x, k );
        printf( "x: %lf, k: %lf, F(x;k): %lf\n", x, k, y );
    }
}