Cumulative Distribution Function

Discrete uniform distribution cumulative distribution function.

The cumulative distribution function for a discrete uniform random variable is

upper F left-parenthesis x right-parenthesis equals StartLayout Enlarged left-brace 1st Row 1st Column 0 2nd Column for x less-than a 2nd Row 1st Column StartFraction left floor x right floor minus a plus 1 Over b minus a plus 1 EndFraction 2nd Column for a less-than-or-equal-to x less-than b 3rd Row 1st Column 1 2nd Column for x greater-than-or-equal-to b EndLayout

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

Usage

var cdf = require( '@stdlib/math/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/math/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 ) );
}