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

Examples

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

var alpha;
var beta;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = randu() * 3.0;
    alpha = randu() * 5.0;
    beta = randu() * 5.0;
    y = logcdf( x, alpha, beta );
    console.log( 'x: %d, α: %d, β: %d, ln(F(x;α,β)): %d', x.toFixed( 4 ), alpha.toFixed( 4 ), beta.toFixed( 4 ), y.toFixed( 4 ) );
}

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 © 2016-2024. The Stdlib Authors.