@stdlib/stats-base-dists-poisson-quantile
v0.2.3TypeScript
Poisson distribution quantile function.
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Quantile Function
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> [Poisson][poisson-distribution] distribution [quantile function][quantile-function].
The [quantile function][quantile-function] for a [Poisson][poisson-distribution] 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
``bash`
npm install @stdlib/stats-base-dists-poisson-quantile
Usage
`javascript`
var quantile = require( '@stdlib/stats-base-dists-poisson-quantile' );
#### quantile( p, lambda )
Evaluates the [quantile function][quantile-function] for a [Poisson][poisson-distribution] distribution with mean parameter lambda at a probability p.
`javascript
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.
`javascript
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.
`javascript
var y = quantile( NaN, 1.0 );
// returns NaN
y = quantile( 0.0, NaN );
// returns NaN
`
If provided a negative lambda, the function returns NaN.
`javascript`
var y = quantile( 0.4, -1.0 );
// returns NaN
If provided lambda = 0, the function evaluates the [quantile function][quantile-function] of a [degenerate distribution][degenerate-distribution] centered at 0.0.
`javascript
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][quantile-function] of a [Poisson][poisson-distribution] distribution with mean parameter lambda.
`javascript
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
`javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var quantile = require( '@stdlib/stats-base-dists-poisson-quantile' );
var opts = {
'dtype': 'float64'
};
var p = uniform( 10, 0.0, 1.0, opts );
var lambda = uniform( 10, 0.0, 10.0, opts );
logEachMap( 'p: %0.4f, λ: %0.4f, Q(p;λ): %0.4f', p, lambda, quantile );
`
*
Notice
This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib].
#### Community
[![Chat][chat-image]][chat-url]
---
License
See [LICENSE][stdlib-license].
Copyright
Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[stdlib]: https://github.com/stdlib-js/stdlib
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[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
[deno-url]: https://github.com/stdlib-js/stats-base-dists-poisson-quantile/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-base-dists-poisson-quantile/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-base-dists-poisson-quantile/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-base-dists-poisson-quantile/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-base-dists-poisson-quantile/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-base-dists-poisson-quantile/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-base-dists-poisson-quantile/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-poisson-quantile/main/LICENSE
[poisson-distribution]: https://en.wikipedia.org/wiki/Poisson_distribution
[quantile-function]: https://en.wikipedia.org/wiki/Quantile_function
[degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution