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About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

Cumulative Distribution Function

NPM version Build Status Coverage Status

Poisson distribution cumulative distribution function.

The cumulative distribution function for a Poisson random variable is

$$F(x;\lambda) = \begin{cases} 0 & \text{ for } x \le 0 \\ e^{-\lambda} \sum_{i=0}^{\lfloor x\rfloor} \frac{\lambda^i}{i!} & \text{ for } x > 0 \end{cases}$$

where lambda is the mean parameter. Internally, the module evaluates the CDF by evaluating the upper regularized gamma function at input values lambda and floor( x ) + 1.

Usage

import cdf from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-poisson-cdf@esm/index.mjs';

You can also import the following named exports from the package:

import { factory } from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-poisson-cdf@esm/index.mjs';

cdf( x, lambda )

Evaluates the cumulative distribution function for a Poisson distribution with mean parameter lambda.

var y = cdf( 2.0, 0.5 );
// returns ~0.986

y = cdf( 2.0, 10.0 );
// returns ~0.003

y = cdf( -1.0, 4.0 );
// returns 0.0

If provided NaN as any argument, the function returns NaN.

var y = cdf( NaN, 1.0 );
// returns NaN

y = cdf( 0.0, NaN );
// returns NaN

If provided lambda < 0, the function returns NaN.

var y = cdf( 2.0, -1.0 );
// returns NaN

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

var y = cdf( -2.0, 0.0 );
// returns 0.0

y = cdf( 0.0, 0.0 );
// returns 1.0

y = cdf( 10.0, 0.0 );
// returns 1.0

cdf.factory( lambda )

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

var mycdf = cdf.factory( 5.0 );
var y = mycdf( 3.0 );
// returns ~0.265

y = mycdf( 8.0 );
// returns ~0.932

Examples

<!DOCTYPE html>
<html lang="en">
<body>
<script type="module">

import randu from 'https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randu@esm/index.mjs';
import cdf from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-poisson-cdf@esm/index.mjs';

var lambda;
var x;
var y;
var i;

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

</script>
</body>
</html>

Notice

This package is part of stdlib, a standard library 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.