@stdlib/stats-base-dists-binomial-cdf

Cumulative Distribution Function

Binomial distribution cumulative distribution function.

The cumulative distribution function for a binomial random variable is

where n is the number of trials and p is the success probability. The CDF can be equivalently expressed as

where I is the lower regularized incomplete beta function.

Installation

npm install @stdlib/stats-base-dists-binomial-cdf

Usage

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

cdf( x, n, p )

Evaluates the cumulative distribution function for a binomial distribution with number of trials n and success probability p.

var y = cdf( 3.0, 20, 0.2 );
// returns ~0.411

y = cdf( 21.0, 20, 0.2 );
// returns 1.0

y = cdf( 5.0, 10, 0.4 );
// returns ~0.834

y = cdf( 0.0, 10, 0.4 );
// returns ~0.006

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

var y = cdf( NaN, 20, 0.5 );
// returns NaN

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

y = cdf( 0.0, 20, NaN );
// returns NaN

If provided a number of trials n which is not a nonnegative integer, the function returns NaN.

var y = cdf( 2.0, 1.5, 0.5 );
// returns NaN

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

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

var y = cdf( 2.0, 20, -1.0 );
// returns NaN

y = cdf( 2.0, 20, 1.5 );
// returns NaN

cdf.factory( n, p )

Returns a function for evaluating the cumulative distribution function of a binomial distribution with number of trials n and success probability p.

var mycdf = cdf.factory( 10, 0.5 );

var y = mycdf( 3.0 );
// returns ~0.172

y = mycdf( 1.0 );
// returns ~0.011

Examples

var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var cdf = require( '@stdlib/stats-base-dists-binomial-cdf' );

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

for ( i = 0; i < 10; i++ ) {
    x = randu() * 20.0;
    n = round( randu() * 100.0 );
    p = randu();
    y = cdf( x, n, p );
    console.log( 'x: %d, n: %d, p: %d, F(x;n,p): %d', x.toFixed( 4 ), n, p.toFixed( 4 ), y.toFixed( 4 ) );
}

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Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

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License

See LICENSE.

Copyright

Copyright © 2016-2021. The Stdlib Authors.