## 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!

# Kurtosis

Hypergeometric distribution excess kurtosis.

Imagine a scenario with a population of size `N`

, of which a subpopulation of size `K`

can be considered successes. We draw `n`

observations from the total population. Defining the random variable `X`

as the number of successes in the `n`

draws, `X`

is said to follow a hypergeometric distribution. The excess kurtosis for a hypergeometric random variable is

## Installation

`npm install @stdlib/stats-base-dists-hypergeometric-kurtosis`

## Usage

`var kurtosis = require( '@stdlib/stats-base-dists-hypergeometric-kurtosis' );`

#### kurtosis( N, K, n )

Returns the excess kurtosis of a hypergeometric distribution with parameters `N`

(population size), `K`

(subpopulation size), and `n`

(number of draws).

```
var v = kurtosis( 16, 11, 4 );
// returns ~-0.326
v = kurtosis( 4, 2, 2 );
// returns 0.0
```

If provided `NaN`

as any argument, the function returns `NaN`

.

```
var v = kurtosis( NaN, 10, 4 );
// returns NaN
v = kurtosis( 20, NaN, 4 );
// returns NaN
v = kurtosis( 20, 10, NaN );
// returns NaN
```

If provided a population size `N`

, subpopulation size `K`

, or draws `n`

which is not a nonnegative integer, the function returns `NaN`

.

```
var v = kurtosis( 10.5, 5, 2 );
// returns NaN
v = kurtosis( 10, 1.5, 2 );
// returns NaN
v = kurtosis( 10, 5, -2.0 );
// returns NaN
```

If the number of draws `n`

or the subpopulation size `K`

exceed population size `N`

, the function returns `NaN`

.

```
var v = kurtosis( 10, 5, 12 );
// returns NaN
v = kurtosis( 10, 12, 5 );
// returns NaN
```

## Examples

```
var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var kurtosis = require( '@stdlib/stats-base-dists-hypergeometric-kurtosis' );
var v;
var i;
var N;
var K;
var n;
for ( i = 0; i < 10; i++ ) {
N = round( randu() * 20 );
K = round( randu() * N );
n = round( randu() * K );
v = kurtosis( N, K, n );
console.log( 'N: %d, K: %d, n: %d, Kurt(X;N,K,n): %d', N, K, n, v.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.

#### Community

## License

See LICENSE.

## Copyright

Copyright © 2016-2024. The Stdlib Authors.