README.md

Cumulative Distribution Function

Beta distribution cumulative distribution function.

The cumulative distribution function for a beta random variable is

$$F(x;\alpha,\beta) = \frac{\mathop{\mathrm{Beta}}(x;\alpha,\beta)}{\mathop{\mathrm{Beta}}(\alpha,\beta)}$$

where alpha > 0 is the first shape parameter and beta > 0 is the second shape parameter. In the definition, Beta( x; a, b ) denotes the lower incomplete beta function and Beta( a, b ) the beta function.

Usage

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

cdf( x, alpha, beta )

Evaluates the cumulative distribution function (CDF) for a beta distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

var y = cdf( 0.5, 1.0, 1.0 );
// returns 0.5

y = cdf( 0.5, 2.0, 4.0 );
// returns ~0.813

y = cdf( 0.2, 2.0, 2.0 );
// returns ~0.104

y = cdf( 0.8, 4.0, 4.0 );
// returns ~0.967

y = cdf( -0.5, 4.0, 2.0 );
// returns 0.0

y = cdf( -Infinity, 4.0, 2.0 );
// returns 0.0

y = cdf( 1.5, 4.0, 2.0 );
// returns 1.0

y = cdf( +Infinity, 4.0, 2.0 );
// returns 1.0

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

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

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

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

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

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

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

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

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

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

cdf.factory( alpha, beta )

Returns a function for evaluating the cumulative distribution function for a beta distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

var mycdf = cdf.factory( 0.5, 0.5 );

var y = mycdf( 0.8 );
// returns ~0.705

y = mycdf( 0.3 );
// returns ~0.369

Examples

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

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

logEachMap( 'x: %0.4f, α: %0.4f, β: %0.4f, F(x;α,β): %0.4f', x, alpha, beta, cdf );

---

C APIs

Usage

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

stdlib_base_dists_beta_cdf( x, alpha, beta )

Returns the differential cdf of a beta distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

double y = stdlib_base_dists_beta_cdf( 0.5, 1.0, 1.0 );
// returns 0.5

The function accepts the following arguments:

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

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

Examples

#include "stdlib/stats/base/dists/beta/cdf.h"
#include "stdlib/constants/float64/eps.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 alpha;
    double beta;
    double x;
    double y;
    int i;

    for ( i = 0; i < 10; i++ ) {
        alpha = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 5.0 );
        beta = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 5.0 );
        x = random_uniform( 0.0, 1.0 );
        y = stdlib_base_dists_beta_cdf( x, alpha, beta );
        printf( "x: %lf, α: %lf, β: %lf, F(x;α,β): %lf\n", x, alpha, beta, y );
    }
}