Probability Density Function

Triangular distribution probability density function (PDF).

The probability density function (PDF) for a triangular random variable is

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

Installation

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

Usage

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

pdf( x, a, b, c )

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

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

y = pdf( 0.5, -1.0, 1.0, 0.5 );
// returns 1.0

y = pdf( -10.0, -20.0, 0.0, -2.0 );
// returns ~0.056

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

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

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

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

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

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

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

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

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

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

pdf.factory( a, b, c )

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

var mypdf = pdf.factory( 0.0, 10.0, 5.0 );
var y = mypdf( 2.0 );
// returns 0.08

y = mypdf( 12.0 );
// returns 0.0

Examples

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

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 = pdf( 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.