Quantile Function

Beta prime distribution quantile function.

The quantile function for a beta prime random variable with first shape parameter α > 0 and second shape parameter β > 0 is

upper Q left-parenthesis p semicolon alpha comma beta right-parenthesis equals StartFraction upper G Superscript negative 1 Baseline left-parenthesis p right-parenthesis Over 1 minus upper G Superscript negative 1 Baseline left-parenthesis p right-parenthesis EndFraction

for 0 <= p <= 1, where G^-1 denotes the quantile function of a beta random variable with parameters α and β.

Usage

var quantile = require( '@stdlib/math/base/dists/betaprime/quantile' );

quantile( p, alpha, beta )

Evaluates the quantile function for a beta prime distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

var y = quantile( 0.8, 2.0, 1.0 );
// returns ~2.994

y = quantile( 0.5, 4.0, 2.0 );
// returns ~1.836

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

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

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

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

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

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

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

If provided alpha <= 0, the function returns NaN.

var y = quantile( 0.4, -1.0, 1.0 );
// returns NaN

y = quantile( 0.4, 0.0, 1.0 );
// returns NaN

If provided beta <= 0, the function returns NaN.

var y = quantile( 0.4, 1.0, -1.0 );
// returns NaN

y = quantile( 0.4, 1.0, 0.0 );
// returns NaN

quantile.factory( alpha, beta )

Returns a function for evaluating the quantile function of a beta prime distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

var myQuantile = quantile.factory( 2.0, 2.0 );

var y = myQuantile( 0.8 );
// returns ~2.483

y = myQuantile( 0.4 );
// returns ~0.763

Examples

var randu = require( '@stdlib/random/base/randu' );
var EPS = require( '@stdlib/constants/math/float64-eps' );
var quantile = require( '@stdlib/math/base/dists/betaprime/quantile' );

var alpha;
var beta;
var p;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    p = randu();
    alpha = ( randu()*5.0 ) + EPS;
    beta = ( randu()*5.0 ) + EPS;
    y = quantile( p, alpha, beta );
    console.log( 'p: %d, α: %d, β: %d, Q(p;α,β): %d', p.toFixed( 4 ), alpha.toFixed( 4 ), beta.toFixed( 4 ), y.toFixed( 4 ) );
}