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.

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 ) );
}

C APIs

Usage

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

stdlib_base_dists_triangular_pdf( x, a, b, c )

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

double y = stdlib_base_dists_triangular_pdf( 0.5, -1.0, 1.0, 0.0 );
// returns 0.5

The function accepts the following arguments:

x: [in] double input value.
a: [in] double lower limit.
b: [in] double upper limit.
c: [in] double mode.

double stdlib_base_dists_triangular_pdf( const double x, const double a, const double b, const double c );

Examples

#include "stdlib/stats/base/dists/triangular/pdf.h"
#include "stdlib/constants/float64/eps.h"
#include <stdlib.h>
#include <stdio.h>
#include <math.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 x;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        x = random_uniform( 0.0, 30.0 );
        a = random_uniform( 0.0, 10.0 );
        b = random_uniform( a+STDLIB_CONSTANT_FLOAT64_EPS, 40.0 );
        c = a + random_uniform( 0.0, b - a );
        y = stdlib_base_dists_triangular_pdf( x, a, b, c );
        printf( "x: %lf, a: %lf, b: %lf, c: %lf, f(x;a,b,c): %lf\n", x, a, b, c, y );
    }
}