Cumulative Distribution Function

Geometric distribution cumulative distribution function.

The cumulative distribution function for a geometric random variable is

upper F left-parenthesis x semicolon p right-parenthesis equals StartLayout Enlarged left-brace 1st Row 1st Column 0 2nd Column for x less-than 0 2nd Row 1st Column 1 minus left-parenthesis 1 minus p right-parenthesis Superscript left floor x right floor plus 1 Baseline 2nd Column otherwise EndLayout

where 0 <= p <= 1 is the success probability. x denotes the number of failures before the first success.

Usage

var cdf = require( '@stdlib/math/base/dists/geometric/cdf' );

cdf( x, p )

Evaluates the cumulative distribution function for a geometric distribution with success probability p.

var y = cdf( 2.0, 0.5 );
// returns 0.875

y = cdf( 2.0, 0.1 );
// returns ~0.271

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

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

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

If provided a success probability p outside of [0,1], the function returns NaN.

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

y = cdf( 2.0, 1.5 );
// returns NaN

cdf.factory( p )

Returns a function for evaluating the cumulative distribution function of a geometric distribution with success probability p

var mycdf = cdf.factory( 0.5 );
var y = mycdf( 3.0 );
// returns 0.9375

y = mycdf( 1.0 );
// returns 0.75

Examples

var randu = require( '@stdlib/random/base/randu' );
var cdf = require( '@stdlib/math/base/dists/geometric/cdf' );

var p;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = randu() * 5.0;
    p = randu();
    y = cdf( x, p );
    console.log( 'x: %d, p: %d, F(x;p): %d', x.toFixed( 4 ), p.toFixed( 4 ), y.toFixed( 4 ) );
}