Quantile Function

Planck (discrete exponential) distribution quantile function.

The quantile function for a Planck random variable is

for 0 < p < 1 and where λ is the shape parameter.

Usage

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

quantile( p, lambda )

Evaluates the quantile function for a Planck distribution with shape parameter lambda at a probability p.

var y = quantile( 0.8, 0.4 );
// returns 4

y = quantile( 0.5, 1.4 );
// returns 0

y = quantile( 0.9, 2.1 );
// returns 1

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

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

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

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

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

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

If provided a shape parameter lambda which is nonpositive, the function returns NaN.

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

quantile.factory( lambda )

Returns a function for evaluating the quantile function for a Planck distribution with shape parameter lambda.

var myquantile = quantile.factory( 0.4 );
var y = myquantile( 0.4 );
// returns 1

y = myquantile( 0.8 );
// returns 4

y = myquantile( 1.0 );
// returns Infinity

Examples

var uniform = require( '@stdlib/random/array/uniform' );
var quantile = require( '@stdlib/stats/base/dists/planck/quantile' );

var lambda = uniform( 10, 0.1, 10.0 );
var p = uniform( 10, 0.0, 1.0 );

var y;
var i;
for ( i = 0; i < lambda.length; i++ ) {
    y = quantile( p[ i ], lambda[ i ] );
    console.log( 'p: %d, λ: %d, Q(p;λ): %d', p[ i ].toFixed( 4 ), lambda[ i ].toFixed( 4 ), y.toFixed( 4 ) );
}