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README.md |
Quantile Function
Chi distribution quantile function.
The quantile function for a chi random variable is
for 0 <= p < 1
, where k
is the degrees of freedom and P^{-1}
is the inverse of the lower, regularized incomplete gamma function.
Usage
var quantile = require( '@stdlib/stats/base/dists/chi/quantile' );
quantile( p, k )
Evaluates the quantile function for a chi distribution with degrees of freedom k
.
var y = quantile( 0.8, 1.0 );
// returns ~1.282
y = quantile( 0.5, 4.0 );
// returns ~1.832
y = quantile( 0.8, 0.1 );
// returns ~0.116
If provided a probability p
outside the interval [0,1]
, the function returns NaN
.
var y = quantile( 1.9, 1.0 );
// returns NaN
y = quantile( -0.1, 1.0 );
// returns NaN
If provided NaN
as any argument, the function returns NaN
.
var y = quantile( NaN, 1.0 );
// returns NaN
y = quantile( 0.2, NaN );
// returns NaN
If provided k < 0
, the function returns NaN
.
var y = quantile( 0.4, -1.0 );
// returns NaN
If provided k = 0
, the function evaluates the quantile function of a degenerate distribution centered at 0
.
var y = quantile( 0.3, 0.0 );
// returns 0.0
y = quantile( 0.9, 0.0 );
// returns 0.0
quantile.factory( k )
Returns a function for evaluating the quantile function of a chi distribution with degrees of freedom k
.
var myquantile = quantile.factory( 0.4 );
var y = myquantile( 0.9 );
// returns ~1.1
y = myquantile( 1.0 );
// returns Infinity
Examples
var randu = require( '@stdlib/random/base/randu' );
var quantile = require( '@stdlib/stats/base/dists/chi/quantile' );
var k;
var p;
var y;
var i;
for ( i = 0; i < 20; i++ ) {
p = randu();
k = randu() * 10.0;
y = quantile( p, k );
console.log( 'p: %d, k: %d, Q(p;k): %d', p.toFixed( 4 ), k.toFixed( 4 ), y.toFixed( 4 ) );
}