Quantile Function

Triangular distribution quantile function.

The quantile 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-quantile

Usage

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

quantile( p, a, b, c )

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

var y = quantile( 0.9, -1.0, 1.0, 0.0 );
// returns ~0.553

y = quantile( 0.1, -1.0, 1.0, 0.5 );
// returns ~-0.452

y = quantile( 0.1, -20.0, 0.0, -2.0 );
// returns -14.0

y = quantile( 0.8, 0.0, 20.0, 0.0 );
// returns ~11.056

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

var y = quantile( 1.9, 0.0, 1.0, 0.5 );
// returns NaN

y = quantile( -0.1, 0.0, 1.0, 0.5 );
// returns NaN

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

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

y = quantile( 0.1, NaN, 1.0, 0.5 );
// returns NaN

y = quantile( 0.1, 0.0, NaN, 0.5 );
// returns NaN

y = quantile( 0.1, 0.0, 1.0, NaN );
// returns NaN

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

var y = quantile( 0.1, 1.0, 0.0, 1.5 );
// returns NaN

y = quantile( 0.1, 1.0, 0.0, -1.0 );
// returns NaN

y = quantile( 0.1, 0.0, -1.0, 0.5 );
// returns NaN

quantile.factory( a, b, c )

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

var myquantile = quantile.factory( 2.0, 4.0, 2.5 );
var y = myquantile( 0.4 );
// returns ~2.658

y = myquantile( 0.8 );
// returns ~3.225

Examples

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

var a;
var b;
var c;
var p;
var y;
var i;

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

C APIs

Usage

#include "stdlib/stats/base/dists/triangular/quantile.h"

stdlib_base_dists_triangular_quantile( p, a, b, c )

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

double out = stdlib_base_dists_triangular_quantile( 0.9, -1.0, 1.0, 0.0 );
// returns ~0.553

The function accepts the following arguments:

• p: [in] double input probability.
• a: [in] double minimum support.
• b: [in] double maximum support.
• c: [in] double mode.

double stdlib_base_dists_triangular_quantile( const double p, const double a, const double b, const double c );

Examples

#include "stdlib/stats/base/dists/triangular/quantile.h"
#include <stdlib.h>
#include <stdio.h>

static double random_uniform( const double min, const double max ) {
    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
    return min + ( v*(max-min) );
}

int main( void ) {
    double a;
    double b;
    double c;
    double p;
    double v;
    int i;

    for ( i = 0; i < 25; i++ ) {
        p = random_uniform( 0.0, 1.0 );
        a = random_uniform( 0.0, 10.0 );
        b = random_uniform( a, a+10.0 );
        c = random_uniform( a, b );
        v = stdlib_base_dists_triangular_quantile( p, a, b, c );
        printf( "p: %lf, a: %lf, b: %lf, c: %lf, Q(p;a,b,c): %lf\n", p, a, b, c, v );
    }
}

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.