Cumulative Distribution Function

Triangular distribution cumulative distribution function.

The cumulative distribution function for a triangular random variable is

where a is the lower limit, b is the upper limit, and c is the mode.

Installation

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

Usage

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

cdf( x, a, b, c )

Evaluates the cumulative distribution function (CDF) for a triangular distribution with parameters a (lower limit), b (upper limit) and c (mode).

var y = cdf( 0.5, -1.0, 1.0, 0.0 );
// returns 0.875

y = cdf( 0.5, -1.0, 1.0, 0.5 );
// returns 0.75

y = cdf( -10.0, -20.0, 0.0, -2.0 );
// returns ~0.278

y = cdf( -2.0, -1.0, 1.0, 0.0 );
// returns 0.0

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

var y = cdf( NaN, 0.0, 1.0, 0.5 );
// returns NaN

y = cdf( 0.0, NaN, 1.0, 0.5 );
// returns NaN

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

y = cdf( 2.0, 1.0, 0.0, NaN );
// returns NaN

If provided parameters not satisfying a <= c <= b, the function returns NaN.

var y = cdf( 2.0, 1.0, 0.0, 1.5 );
// returns NaN

y = cdf( 2.0, 1.0, 0.0, -1.0 );
// returns NaN

y = cdf( 2.0, 0.0, -1.0, 0.5 );
// returns NaN

cdf.factory( a, b, c )

Returns a function for evaluating the cumulative distribution function of a triangular distribution with parameters a (lower limit), b (upper limit) and c (mode).

var mycdf = cdf.factory( 0.0, 10.0, 2.0 );
var y = mycdf( 0.5 );
// returns 0.0125

y = mycdf( 8.0 );
// returns 0.95

Examples

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

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

for ( i = 0; i < 25; i++ ) {
    x = randu() * 30.0;
    a = randu() * 10.0;
    b = a + (randu() * 40.0);
    c = a + ((b-a) * randu());
    y = cdf( x, a, b, c );
    console.log( 'x: %d, a: %d, b: %d, c: %d, F(x;a,b,c): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), c.toFixed( 4 ), y.toFixed( 4 ) );
}

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.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.