Logarithm of Cumulative Distribution Function

Gamma distribution logarithm of cumulative distribution function (CDF).

The cumulative distribution function for a gamma random variable is

where alpha is the shape parameter and beta is the rate parameter of the distribution. gamma is the lower incomplete gamma function.

Installation

npm install @stdlib/stats-base-dists-gamma-logcdf

Usage

var logcdf = require( '@stdlib/stats-base-dists-gamma-logcdf' );

logcdf( x, alpha, beta )

Evaluates the natural logarithm of the cumulative distribution function (CDF) for a gamma distribution with parameters alpha (shape parameter) and beta (rate parameter).

var y = logcdf( 2.0, 0.5, 1.0 );
// returns ~-0.047

y = logcdf( 0.1, 1.0, 1.0 );
// returns ~-2.352

y = logcdf( -1.0, 4.0, 2.0 );
// returns -Infinity

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

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

y = logcdf( 0.0, NaN, 1.0 );
// returns NaN

y = logcdf( 0.0, 1.0, NaN );
// returns NaN

If provided alpha < 0, the function returns NaN.

var y = logcdf( 2.0, -0.5, 1.0 );
// returns NaN

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

var y = logcdf( 2.0, 0.0, 2.0 );
// returns 0.0

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

y = logcdf( 0.0, 0.0, 2.0 );
// returns 0.0

If provided beta <= 0, the function returns NaN.

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

y = logcdf( 2.0, 1.0, -1.0 );
// returns NaN

logcdf.factory( alpha, beta )

Returns a function for evaluating the natural logarithm of the CDF for a gamma distribution with parameters alpha (shape parameter) and beta (rate parameter).

var mylogcdf = logcdf.factory( 3.0, 1.5 );

var y = mylogcdf( 1.0 );
// returns ~-1.655

y = mylogcdf( 4.0 );
// returns ~-0.064

C APIs

Usage

#include "stdlib/stats/base/dists/gamma/logcdf.h"

stdlib_base_dists_gamma_logcdf( x, alpha, beta )

Evaluates the natural logarithm of the cumulative distribution function (CDF) for a gamma distribution with shape parameter alpha and rate parameter beta.

double out = stdlib_base_dists_gamma_logcdf( 2.0, 0.5, 1.0 );
// returns ~-0.047

out = stdlib_base_dists_gamma_logcdf( 0.1, 1.0, 1.0 );
// returns ~-2.352

The function accepts the following arguments:

• x: [in] double input value.
• alpha: [in] double shape parameter.
• beta: [in] double rate parameter.

double stdlib_base_dists_gamma_logcdf( const double x, const double alpha, const double beta );

Examples

#include "stdlib/stats/base/dists/gamma/logcdf.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 alpha;
    double beta;
    double x;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        x = random_uniform( 0.0, 2.0 );
        alpha = random_uniform( 1.0, 10.0 );
        beta = random_uniform( 1.0, 10.0 );
        y = stdlib_base_dists_gamma_logcdf( x, alpha, beta );
        printf( "x: %lf, α: %lf, β: %lf, ln(F(x;α,β)): %lf\n", x, alpha, beta, y );
    }
}

Examples

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

var opts = {
    'dtype': 'float64'
};
var x = uniform( 10, 0.0, 3.0, opts );
var alpha = uniform( 10, 0.0, 5.0, opts );
var beta = uniform( 10, 0.0, 5.0, opts );

logEachMap( 'x: %0.4f, α: %0.4f, β: %0.4f, ln(f(x;α,β)): %0.4f', x, alpha, beta, logcdf );

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

License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.