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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

$$F(x;\lambda) \ge p$$

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

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

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 );
}

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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

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.