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

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

Installation

npm install @stdlib/stats-base-dists-poisson-quantile

Usage

var quantile = require( '@stdlib/stats-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 = myquantile( 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/stats-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 );
}

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.