Probability Density Function

Triangular distribution probability density function (PDF).

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

f left-parenthesis x semicolon a comma b comma c right-parenthesis equals StartLayout Enlarged left-brace 1st Row 1st Column 0 2nd Column for x less-than a 2nd Row 1st Column StartFraction 2 left-parenthesis x minus a right-parenthesis Over left-parenthesis b minus a right-parenthesis left-parenthesis c minus a right-parenthesis EndFraction 2nd Column for a less-than-or-equal-to x less-than c 3rd Row 1st Column StartFraction 2 Over b minus a EndFraction 2nd Column for x equals c 4th Row 1st Column StartFraction 2 left-parenthesis b minus x right-parenthesis Over left-parenthesis b minus a right-parenthesis left-parenthesis b minus c right-parenthesis EndFraction 2nd Column for c less-than x less-than-or-equal-to b 5th Row 1st Column 0 2nd Column for b less-than x EndLayout

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

Usage

var pdf = require( '@stdlib/math/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/math/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 ) );
}