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

0.2.1 • Public • Published

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# Quantile Function

Binomial distribution quantile function.

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

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.

## Installation

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

## Usage

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

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

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

```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`.

```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`.

```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`.

```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 of a binomial distribution with number of trials `n` and success probability `p`.

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

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

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

## Examples

```var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var quantile = require( '@stdlib/stats-base-dists-binomial-quantile' );

var r;
var i;
var n;
var p;
var y;

for ( i = 0; i < 10; i++ ) {
r = randu();
n = round( randu() * 100.0 );
p = randu();
y = quantile( r, n, p );
console.log( 'r: %d, n: %d, p: %d, Q(r;n,p): %d', r.toFixed( 4 ), n, p.toFixed( 4 ) );
}```

## 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-binomial-quantile`

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