# npm

## @stdlib/stats-base-dists-triangular-pdf

0.0.8 • Public • Published

# 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.

## Keywords

### Install

`npm i @stdlib/stats-base-dists-triangular-pdf`

stdlib.io

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0.0.8

Apache-2.0

52.4 kB

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