@stdlib/stats-base-dists-negative-binomial-kurtosis
v0.3.1TypeScript
Negative binomial distribution excess kurtosis.
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Published by The Stdlib Authors
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About stdlib...
Kurtosis
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> [Negative binomial][negative-binomial-distribution] distribution [excess kurtosis][kurtosis].
The [excess kurtosis][kurtosis] for a [negative binomial][negative-binomial-distribution] random variable is
where r is the number of successes until experiment is stopped and p is the success probability in each trial. The random variable X denotes the number of failures until the r success is reached.
Installation
``bash`
npm install @stdlib/stats-base-dists-negative-binomial-kurtosis
Usage
`javascript`
var kurtosis = require( '@stdlib/stats-base-dists-negative-binomial-kurtosis' );
#### kurtosis( r, p )
Returns the [excess kurtosis][kurtosis] of a [negative binomial][negative-binomial-distribution] distribution with parameters r (number of successes until experiment is stopped) and p (success probability).
`javascript
var v = kurtosis( 100, 0.2 );
// returns ~0.061
v = kurtosis( 50, 0.5 );
// returns ~0.13
`
If provided NaN as any argument, the function returns NaN.
`javascript
var v = kurtosis( NaN, 0.5 );
// returns NaN
v = kurtosis( 20, NaN );
// returns NaN
`
If provided a r which is not a positive number, the function returns NaN.
`javascript`
var v = kurtosis( -2.0, 0.5 );
// returns NaN
If provided a success probability p outside of [0,1], the function returns NaN.
`javascript
var v = kurtosis( 20, -1.0 );
// returns NaN
v = kurtosis( 20, 1.5 );
// returns NaN
`
Examples
`javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var kurtosis = require( '@stdlib/stats-base-dists-negative-binomial-kurtosis' );
var opts = {
'dtype': 'float64'
};
var r = uniform( 10, 0.0, 100.0, opts );
var p = uniform( 10, 0.0, 1.0, opts );
logEachMap( 'r: %0.4f, p: %0.4f, Kurt(X;r,p): %0.4f', r, p, kurtosis );
`
*
C APIs
$3
`c`
#include "stdlib/stats/base/dists/negative-binomial/kurtosis.h"
#### stdlib_base_dists_negative_binomial_kurtosis( r, p )
Returns the excess kurtosis of a negative binomial distribution.
`c`
double y = stdlib_base_dists_negative_binomial_kurtosis( 100.0, 0.2 );
// returns ~0.061
The function accepts the following arguments:
- r: [in] double number of failures until experiment is stopped.[in] double
- p: success probability.
`c`
double stdlib_base_dists_negative_binomial_kurtosis( const double r, const double p );
$3
`c
#include "stdlib/stats/base/dists/negative-binomial/kurtosis.h"
#include
#include
static double random_uniform( const double min, const double max ) {
double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
return min + ( v*(max-min) );
}
int main( void ) {
double r;
double p;
double y;
int i;
for ( i = 0; i < 10; i++ ) {
r = random_uniform( 1.0, 100.0 );
p = random_uniform( 0.01, 0.99 );
y = stdlib_base_dists_negative_binomial_kurtosis( r, p );
printf( "r: %f, p: %.4f, Kurt(X;r,p): %.4f\n", r, p, y );
}
}
`
*
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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[deno-readme]: https://github.com/stdlib-js/stats-base-dists-negative-binomial-kurtosis/blob/deno/README.md
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[negative-binomial-distribution]: https://en.wikipedia.org/wiki/Negative_binomial_distribution
[kurtosis]: https://en.wikipedia.org/wiki/Kurtosis