README.md

Logarithm of Probability Density Function

Evaluate the natural logarithm of the probability density function (PDF) for a chi distribution.

The probability density function (PDF) for a chi random variable is

$$f(x;\,k) = \frac{2^{{1-k/2}}x^{{k-1}}e^{{-x^{2}/2}}}{\Gamma(k/2)}$$

where k is the degrees of freedom and Γ denotes the gamma function.

Usage

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

logpdf( x, k )

Evaluates the natural logarithm of the probability density function (PDF) for a chi distribution with degrees of freedom k.

var y = logpdf( 0.1, 1.0 );
// returns ~-0.231

y = logpdf( 0.5, 2.0 );
// returns ~-0.818

y = logpdf( -1.0, 4.0 );
// returns -Infinity

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

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

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

If provided k < 0, the function returns NaN.

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

If provided k = 0, the function evaluates the natural logarithm of the PDF for a degenerate distribution centered at 0.

var y = logpdf( 2.0, 0.0 );
// returns -Infinity

y = logpdf( 0.0, 0.0 );
// returns Infinity

logpdf.factory( k )

Returns a function for evaluating the natural logarithm of the PDF for a chi distribution with degrees of freedom k.

var mylogPDF = logpdf.factory( 6.0 );

var y = mylogPDF( 3.0 );
// returns ~-1.086

y = mylogPDF( 1.0 );
// returns ~-2.579

Examples

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

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

logEachMap( 'x: %0.4f, k: %0.4f, ln(f(x;k)): %0.4f', x, k, logpdf );

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C APIs

Usage

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

stdlib_base_dists_chi_logpdf( x, k )

Evaluates the natural logarithm of the probability density function (PDF) for a chi distribution with degrees of freedom k.

double out = stdlib_base_dists_chi_logpdf( 2.0, 2.0 );
// returns ~-1.307

The function accepts the following arguments:

• x: [in] double input value.
• k: [in] double degrees of freedom.

double stdlib_base_dists_chi_logpdf( const double x, const double k );

Examples

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

static double random_uniform( const double min, const double max ) {
    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
    return min + ( v*(max-min) );
}

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

    for ( i = 0; i < 25; i++ ) {
        x = random_uniform( 0.0, 10.0 );
        k = random_uniform( 0.1, 10.0 );
        y = stdlib_base_dists_chi_logpdf( x, k );
        printf( "x: %lf, k: %lf, ln(f(x;k)): %lf\n", x, k, y );
    }
}