Quantile Function

Triangular distribution quantile function.

The quantile function for a Triangular random variable is

upper Q left-parenthesis p semicolon a comma b comma c right-parenthesis equals StartLayout Enlarged left-brace 1st Row 1st Column a plus StartRoot left-parenthesis b minus a right-parenthesis left-parenthesis c minus a right-parenthesis p EndRoot 2nd Column for 0 less-than-or-equal-to p less-than-or-equal-to upper F left-parenthesis c right-parenthesis 2nd Row 1st Column b minus StartRoot left-parenthesis b minus a right-parenthesis left-parenthesis b minus c right-parenthesis left-parenthesis 1 minus p right-parenthesis EndRoot 2nd Column for upper F left-parenthesis c right-parenthesis less-than-or-equal-to p less-than-or-equal-to 1 EndLayout

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

Usage

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