Cumulative Distribution Function

Discrete uniform distribution cumulative distribution function.

The cumulative distribution function for a discrete uniform 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/discrete-uniform/cdf' );

cdf( x, a, b )

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

var y = cdf( 9.0, 0, 10 );
// returns ~0.909

y = cdf( 0.5, -2, 2 );
// returns ~0.6

y = cdf( -Infinity, 2, 4 );
// returns 0.0

y = cdf( Infinity, 2, 4 );
// returns 1.0

If a or b is not an integer value, the function returns NaN.

var y = cdf( 0.2, 1, 5.5 );
// returns NaN

y = cdf( NaN, 0, 1 );
// returns NaN

y = cdf( 0.0, NaN, 1 );
// returns NaN

y = cdf( 0.0, 0, NaN );
// returns NaN

If provided a > b, the function returns NaN.

var y = cdf( 0.5, 3, 2);
// returns NaN

cdf.factory( a, b )

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

var mycdf = cdf.factory( 0, 10 );
var y = mycdf( 0.5 );
// returns ~0.091

y = mycdf( 8.0 );
// returns ~0.818

Examples

var randint = require( '@stdlib/random/base/discrete-uniform' );
var randu = require( '@stdlib/random/base/randu' );
var cdf = require( '@stdlib/stats/base/dists/discrete-uniform/cdf' );

var randa = randint.factory( 0, 10 );
var randb = randint.factory();
var a;
var b;
var x;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    x = randu() * 15.0;
    a = randa();
    b = randb( a, a+randa() );
    v = 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 ), v.toFixed( 4 ) );
}

C APIs

Usage

#include "stdlib/stats/base/dists/discrete-uniform/cdf.h"

stdlib_base_dists_discrete_uniform_cdf( x, a, b )

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

double out = stdlib_base_dists_discrete_uniform_cdf( 9.0, 0, 10 );
// returns ~0.909

The function accepts the following arguments:

x: [in] double input value.
a: [in] int32_t minimum support.
b: [in] int32_t maximum support.

double stdlib_base_dists_discrete_uniform_cdf( const double x, const int32_t a, const int32_t b );

Examples

#include "stdlib/stats/base/dists/discrete-uniform/cdf.h"
#include "stdlib/math/base/special/round.h"
#include <stdint.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 ) {
    int32_t a;
    int32_t b;
    double x;
    double y;
    int i;

    for ( i = 0; i < 10; i++ ) {
        x = random_uniform( -10.0, 10.0 );
        a = stdlib_base_round( random_uniform( 0.0, 10.0 ) );
        b = stdlib_base_round( random_uniform( a, a+10.0 ) );
        y = stdlib_base_dists_discrete_uniform_cdf( x, a, b );
        printf( "x:%lf, a: %d, b: %d, F(X;a,b): %lf\n", x, a, b, y );
    }
}