Quantile Function

Poisson distribution quantile function.

The quantile function for a Poisson random variable returns for 0 <= p <= 1 the smallest nonnegative integer for which

upper F left-parenthesis x semicolon lamda right-parenthesis greater-than-or-equal-to p

where F is the cumulative distribution function (CDF) of a Poisson distribution with mean parameter lambda > 0.

Usage

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

quantile( p, lambda )

Evaluates the quantile function for a Poisson distribution with mean parameter lambda at a probability p.

var y = quantile( 0.5, 2.0 );
// returns 2

y = quantile( 0.9, 4.0 );
// returns 7

y = quantile( 0.1, 200.0 );
// returns 182

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 negative lambda, the function returns NaN.

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

If provided lambda = 0, the function evaluates the quantile function of a degenerate distribution centered at 0.0.

var y = quantile( 0.1, 0.0 );
// returns 0.0

y = quantile( 0.9, 0.0 );
// returns 0.0

quantile.factory( lambda )

Returns a function for evaluating the quantile function of a Poisson distribution with mean parameter lambda.

var myquantile = quantile.factory( 5.0 );
var y = quantile( 0.4 );
// returns 4

y = myquantile( 0.8 );
// returns 7

y = myquantile( 1.0 );
// returns Infinity

Examples

var randu = require( '@stdlib/random/base/randu' );
var quantile = require( '@stdlib/math/base/dists/poisson/quantile' );

var lambda;
var p;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    p = randu();
    lambda = randu() * 10.0;
    y = quantile( p, lambda );
    console.log( 'p: %d, λ: %d, Q(p;λ): %d', p.toFixed( 4 ), lambda.toFixed( 4 ), y );
}