Logarithm of Cumulative Distribution Function

Evaluate the natural logarithm of the cumulative distribution function for a Kumaraswamy's double bounded distribution.

The cumulative distribution function for a Kumaraswamy's double bounded random variable is

where a > 0 is the first shape parameter and b > 0 is the second shape parameter.

Installation

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

Usage

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

logcdf( x, a, b )

Evaluates the natural logarithm of the cumulative distribution function (CDF) for a Kumaraswamy's double bounded distribution with parameters a (first shape parameter) and b (second shape parameter).

var y = logcdf( 0.5, 1.0, 1.0 );
// returns ~-0.693

y = logcdf( 0.5, 2.0, 4.0 );
// returns ~-0.38

y = logcdf( 0.2, 2.0, 2.0 );
// returns ~-2.546

y = logcdf( 0.8, 4.0, 4.0 );
// returns ~-0.13

y = logcdf( -0.5, 4.0, 2.0 );
// returns -Infinity

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

y = logcdf( 1.5, 4.0, 2.0 );
// returns 0.0

y = logcdf( +Infinity, 4.0, 2.0 );
// returns 0.0

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 a <= 0, the function returns NaN.

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

y = logcdf( 2.0, 0.0, 0.5 );
// returns NaN

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

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

y = logcdf( 2.0, 0.5, 0.0 );
// returns NaN

logcdf.factory( a, b )

Returns a function for evaluating the natural logarithm of the cumulative distribution function for a Kumaraswamy's double bounded distribution with parameters a (first shape parameter) and b (second shape parameter).

var mylogcdf = logcdf.factory( 0.5, 0.5 );

var y = mylogcdf( 0.8 );
// returns ~-0.393

y = mylogcdf( 0.3 );
// returns ~-1.116

Notes

• In virtually all cases, using the logpdf or logcdf functions is preferable to manually computing the logarithm of the pdf or cdf, respectively, since the latter is prone to overflow and underflow.

Examples

var EPS = require( '@stdlib/constants-float64-eps' );
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var logcdf = require( '@stdlib/stats-base-dists-kumaraswamy-logcdf' );

var opts = {
    'dtype': 'float64'
};
var x = uniform( 10, 0.0, 1.0, opts );
var a = uniform( 10, EPS, 5.0, opts );
var b = uniform( 10, EPS, 5.0, opts );

logEachMap( 'x: %0.4f, a: %0.4f, b: %0.4f, ln(F(x;a,b)): %0.4f', x, a, b, logcdf );

C APIs

Usage

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

stdlib_base_dists_kumaraswamy_logcdf( x, a, b )

Evaluates the natural logarithm of the cumulative distribution function (CDF) for a Kumaraswamy's double bounded distribution.

double out = stdlib_base_dists_kumaraswamy_logcdf( 0.5, 1.0, 1.0 );
// returns ~-0.693

The function accepts the following arguments:

• x: [in] double input value.
• a: [in] double first shape parameter.
• b: [in] double second shape parameter.

double stdlib_base_dists_kumaraswamy_logcdf( const double x, const double a, const double b );

Examples

#include "stdlib/stats/base/dists/kumaraswamy/logcdf.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 a;
    double b;
    double y;
    int i;
    for ( i = 0; i < 25; i++ ) {
        x = random_uniform( 0, 1.0 );
        a = random_uniform( 0, 5.0 );
        b = random_uniform( 0, 5.0 );
        y = stdlib_base_dists_kumaraswamy_logcdf( x, a, b );
        printf( "x: %lf, a: %lf, b: %lf, ln(F(x;a,b)): %lf\n", x, a, b, y );
    }
}

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.