npm package: @stdlib/stats-base-dists-binomial-quantile
Description: Binomial distribution quantile function.
Author: The Stdlib Authors
Latest version: 0.2.3

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# Quantile Function

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> [Binomial][binomial-distribution] distribution [quantile function][quantile-function].

<section class="intro">

The [quantile function][quantile-function] for a [binomial][binomial-distribution] random variable returns, for any `r` satisfying `0 <= r <= 1`, the value `x` for which the relation

<!-- <equation class="equation" label="eq:binomial_quantile_function" align="center" raw="F(x-1;n,p) < r \le F(x;n,p)" alt="Quantile value for a binomial distribution."> -->

<div class="equation" align="center" data-raw-text="F(x-1;n,p) &lt; r \le F(x;n,p)" data-equation="eq:binomial_quantile_function">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/binomial/quantile/docs/img/equation_binomial_quantile_function.svg" alt="Quantile value for a binomial distribution.">
    <br>
</div>

<!-- </equation> -->

holds, where `F` is the cumulative distribution function (CDF) of a binomial random variable, `n` is the number of trials, and `0 <= p <= 1` is the success probability.

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-base-dists-binomial-quantile
```

</section>

<section class="usage">

## Usage

```javascript
var quantile = require( '@stdlib/stats-base-dists-binomial-quantile' );
```

#### quantile( r, n, p )

Evaluates the [quantile function][quantile-function] for a [binomial][binomial-distribution] distribution with number of trials `n` and success probability `p` at value `r`.

```javascript
var y = quantile( 0.4, 20, 0.2 );
// returns 3

y = quantile( 0.8, 20, 0.2 );
// returns 5

y = quantile( 0.5, 10, 0.4 );
// returns 4

y = quantile( 0.0, 10, 0.4 );
// returns 0

y = quantile( 1.0, 10, 0.4 );
// returns 10
```

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

```javascript
var y = quantile( NaN, 20, 0.5 );
// returns NaN

y = quantile( 0.2, NaN, 0.5 );
// returns NaN

y = quantile( 0.2, 20, NaN );
// returns NaN
```

If provided a number of trials `n` which is not a nonnegative integer, the function returns `NaN`.

```javascript
var y = quantile( 0.5, 1.5, 0.5 );
// returns NaN

y = quantile( 0.5, -2.0, 0.5 );
// returns NaN
```

If provided a success probability `p` outside of `[0,1]`, the function returns `NaN`.

```javascript
var y = quantile( 0.5, 20, -1.0 );
// returns NaN

y = quantile( 0.5, 20, 1.5 );
// returns NaN
```

#### quantile.factory( n, p )

Returns a function for evaluating the [quantile function][quantile-function] of a [binomial][binomial-distribution] distribution with number of trials `n` and success probability `p`.

```javascript
var myquantile = quantile.factory( 10, 0.5 );

var y = myquantile( 0.1 );
// returns 3

y = myquantile( 0.9 );
// returns 7
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var quantile = require( '@stdlib/stats-base-dists-binomial-quantile' );

var opts = {
    'dtype': 'float64'
};
var r = uniform( 10, 0.0, 1.0, opts );
var n = discreteUniform( 10, 0, 100, opts );
var p = uniform( 10, 0.0, 1.0, opts );

logEachMap( 'r: %0.4f, n: %0.4f, p: %0.4f, Q(r;n,p): %0.4f', r, n, p, quantile );
```

</section>

<!-- /.examples -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## 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].

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---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-binomial-quantile/main/LICENSE

[binomial-distribution]: https://en.wikipedia.org/wiki/Binomial_distribution

[quantile-function]: https://en.wikipedia.org/wiki/Quantile_function

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