Quantile Function
Pareto (Type I) distribution quantile function.
The quantile function for a Pareto (Type I) random variable is
for 0 <= p < 1
, where alpha
is the shape parameter and beta
is the scale parameter.
Usage
var quantile = require( '@stdlib/stats/base/dists/pareto-type1/quantile' );
quantile( p, alpha, beta )
Evaluates the quantile function for a Pareto (Type I) distribution with parameters alpha
(shape parameter) and beta
( scale parameter).
var y = quantile( 0.8, 2.0, 1.0 );
// returns ~2.236
y = quantile( 0.8, 1.0, 10.0 );
// returns ~50.0
y = quantile( 0.1, 1.0, 10.0 );
// returns ~11.111
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 Pareto (Type I) distribution with parameters alpha
(shape parameter) and beta
( scale parameter).
var myquantile = quantile.factory( 2.5, 0.5 );
var y = myquantile( 0.5 );
// returns ~0.66
y = myquantile( 0.8 );
// returns ~0.952
Examples
var randu = require( '@stdlib/random/base/randu' );
var quantile = require( '@stdlib/stats/base/dists/pareto-type1/quantile' );
var alpha;
var beta;
var p;
var y;
var i;
for ( i = 0; i < 10; i++ ) {
p = randu();
alpha = randu() * 5.0;
beta = randu() * 5.0;
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 ) );
}