# @stdlib/stats-base-dists-poisson-quantile

0.2.2 • Public • Published

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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

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.

## Package Sidebar

### Install

`npm i @stdlib/stats-base-dists-poisson-quantile`

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