Triangular

Triangular distribution.

Installation

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

Usage

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

triangular

Triangular distribution.

var dist = triangular;
// returns {...}

The namespace contains the following distribution functions:

• cdf( x, a, b, c ): triangular distribution cumulative distribution function.
• logcdf( x, a, b, c ): triangular distribution logarithm of cumulative distribution function.
• logpdf( x, a, b, c ): triangular distribution logarithm of probability density function (PDF).
• mgf( t, a, b, c ): triangular distribution moment-generating function (MGF).
• pdf( x, a, b, c ): triangular distribution probability density function (PDF).
• quantile( p, a, b, c ): triangular distribution quantile function.

The namespace contains the following functions for calculating distribution properties:

• entropy( a, b, c ): triangular distribution differential entropy.
• kurtosis( a, b, c ): triangular distribution excess kurtosis.
• mean( a, b, c ): triangular distribution expected value.
• median( a, b, c ): triangular distribution median.
• mode( a, b, c ): triangular distribution mode.
• skewness( a, b, c ): triangular distribution skewness.
• stdev( a, b, c ): triangular distribution standard deviation.
• variance( a, b, c ): triangular distribution variance.

The namespace contains a constructor function for creating a triangular distribution object.

• Triangular( [a, b, c] ): triangular distribution constructor.

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

var dist = new Triangular( 2.0, 4.0, 3.0 );

var y = dist.quantile( 0.5 );
// returns 3.0

y = dist.quantile( 1.9 );
// returns NaN

Examples

var discreteUniform = require( '@stdlib/random-base-discrete-uniform' );
var triangular = require( '@stdlib/stats-base-dists-triangular' );

// Scenario: Modeling completion time for a software development task

// Define the distribution parameters (in hours):
var a = 1.5; // Minimum time (best-case scenario)
var b = 4.5; // Maximum time (worst-case scenario)
var c = discreteUniform( 2, 4 ); // Most likely time (mode)
console.log( 'a: %d, b: %d, c: %d', a, b, c );

// Expected (mean) completion time:
var mean = triangular.mean( a, b, c );
console.log( '\nExpected completion time: %d hours', mean );

// Median completion time:
var median = triangular.median( a, b, c );
console.log( 'Median completion time: %d hours', median );

// Variance in completion time:
var variance = triangular.variance( a, b, c );
console.log( 'Variance in completion time: %d hours^2', variance );

// Probability of completing the task within 3 hours:
var x = 3.0;
var prob = triangular.cdf( x, a, b, c );
console.log( '\nProbability of completing within %d hours: %d', x, prob );

// 90th percentile of completion time:
var p = 0.9;
var percentile = triangular.quantile( p, a, b, c );
console.log( '90% of tasks will be completed within %d hours', percentile );

// Relative likelihood of completing the task in exactly 2.5 hours:
x = 2.5;
var likelihood = triangular.pdf( x, a, b, c );
console.log( '\nRelative likelihood of completing in exactly %d hours: %d', x, likelihood );

// Skewness to understand the distribution's shape:
var skewness = triangular.skewness( a, b, c );
console.log( '\nSkewness of completion times: %d', skewness );
if ( skewness > 0 ) {
    console.log( 'The distribution is right-skewed, suggesting occasional longer completion times.' );
} else if ( skewness < 0 ) {
    console.log( 'The distribution is left-skewed, suggesting occasional shorter completion times.' );
} else {
    console.log( 'The distribution is symmetric.' );
}

// Entropy as a measure of uncertainty in the estimate:
var entropy = triangular.entropy( a, b, c );
console.log( '\nEntropy of the distribution: %d nats', entropy );
console.log( 'Higher entropy indicates more uncertainty in completion times.' );

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 © 2016-2026. The Stdlib Authors.