Cumulative Distribution Function

Bradford distribution cumulative distribution function (CDF).

The cumulative distribution function (CDF) for a Bradford random variable is

where c > 0 is the shape parameter of the distribution.

Installation

npm install @stdlib/stats-base-dists-bradford-cdf

Usage

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

cdf( x, c )

Evaluates the cumulative distribution function (CDF) for a Bradford distribution with shape parameter c at a value x.

var y = cdf( 0.1, 0.1 );
// returns ~0.104

y = cdf( 0.5, 5.0 );
// returns ~0.699

y = cdf( 1.0, 10.0 );
// returns 1.0

y = cdf( -0.5, 1.0 );
// returns 0.0

y = cdf( 2.0, 1.0 );
// 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 a shape parameter c <= 0, the function returns NaN.

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

y = cdf( 0.5, -5.0 );
// returns NaN

cdf.factory( c )

Returns a function for evaluating the CDF of a Bradford distribution with shape parameter c.

var myCDF = cdf.factory( 5.0 );
var y = myCDF( 0.5 );
// returns ~0.699

y = myCDF( 1.0 );
// returns 1.0

Examples

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

var opts = {
    'dtype': 'float64'
};
var x = uniform( 10, 0.0, 1.0, opts );
var c = uniform( 10, 0.1, 10.0, opts );

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

C APIs

Usage

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

stdlib_base_dists_bradford_cdf( x, c )

Evaluates the cumulative distribution function for a Bradford distribution.

double out = stdlib_base_dists_bradford_cdf( 0.5, 5.0 );
// returns ~0.699

The function accepts the following arguments:

• x: [in] double input value.
• c: [in] double shape parameter.

double stdlib_base_dists_bradford_cdf( const double x, const double c );

Examples

#include "stdlib/stats/base/dists/bradford/cdf.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 c;
    double y;
    int i;

    for ( i = 0; i < 10; i++ ) {
        x = random_uniform( 0.0, 1.0 );
        c = random_uniform( 0.01, 10.0 );
        y = stdlib_base_dists_bradford_cdf( x, c );
        printf( "x: %lf, c: %lf, F(x;c): %lf\n", x, c, 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.