Cumulative Distribution Function

Arcsine distribution cumulative distribution function.

The cumulative distribution function for an arcsine random variable is

where a is the minimum support and b is the maximum support. The parameters must satisfy a < b.

Usage

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

cdf( x, a, b )

Evaluates the cumulative distribution function (CDF) for an arcsine distribution with parameters a (minimum support) and b (maximum support).

var y = cdf( 9.0, 0.0, 10.0 );
// returns ~0.795

y = cdf( 0.5, 0.0, 2.0 );
// returns ~0.333

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

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

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

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

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

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

If provided a >= b, the function returns NaN.

var y = cdf( 1.0, 2.5, 2.0 );
// returns NaN

cdf.factory( a, b )

Returns a function for evaluating the cumulative distribution function of an arcsine distribution with parameters a (minimum support) and b (maximum support).

var mycdf = cdf.factory( 0.0, 10.0 );
var y = mycdf( 0.5 );
// returns ~0.144

y = mycdf( 8.0 );
// returns ~0.705

Examples

var randu = require( '@stdlib/random/base/randu' );
var cdf = require( '@stdlib/stats/base/dists/arcsine/cdf' );

var a;
var b;
var x;
var y;
var i;

for ( i = 0; i < 25; i++ ) {
    x = ( randu()*20.0 ) - 10.0;
    a = ( randu()*20.0 ) - 20.0;
    b = a + ( randu()*40.0 );
    y = cdf( x, a, b );
    console.log( 'x: %d, a: %d, b: %d, F(x;a,b): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), y.toFixed( 4 ) );
}

C APIs

Usage

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

stdlib_base_dists_arcsine_cdf( x, a, b )

Evaluates the cumulative distribution function (CDF) for an arcsine distribution.

double out = stdlib_base_dists_arcsine_cdf( 0.5, 0.0, 2.0 );
// returns ~0.333

The function accepts the following arguments:

x: [in] double input value.
a: [in] double minimum support.
b: [in] double maximum support.

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

Examples

#include "stdlib/stats/base/dists/arcsine/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 a;
    double b;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        x = random_uniform( -10.0, 10.0 );
        a = random_uniform( -20.0, 0.0 );
        b = random_uniform( a, a+40.0 );
        y = stdlib_base_dists_arcsine_cdf( x, a, b );
        printf( "x: %lf, a: %lf, b: %lf, F(x;a,b): %lf\n", x, a, b, y );
    }
}