Kurtosis

Erlang distribution excess kurtosis.

The excess kurtosis for an Erlang random variable with shape k and rate λ is

Installation

npm install @stdlib/stats-base-dists-erlang-kurtosis

Usage

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

kurtosis( k, lambda )

Returns the excess kurtosis of an Erlang distribution with parameters k (shape parameter) and lambda (rate parameter).

var v = kurtosis( 1, 1.0 );
// returns 6.0

v = kurtosis( 4, 12.0 );
// returns 1.5

v = kurtosis( 8, 2.0 );
// returns 0.75

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

var v = kurtosis( NaN, 2.0 );
// returns NaN

v = kurtosis( 2.0, NaN );
// returns NaN

If not provided a positive integer for k, the function returns NaN.

var v = kurtosis( 1.8, 1.0 );
// returns NaN

v = kurtosis( -1.0, 1.0 );
// returns NaN

If provided lambda <= 0, the function returns NaN.

var v = kurtosis( 2, 0.0 );
// returns NaN

v = kurtosis( 2, -1.0 );
// returns NaN

Examples

var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var EPS = require( '@stdlib/constants-float64-eps' );
var kurtosis = require( '@stdlib/stats-base-dists-erlang-kurtosis' );

var lambda;
var k;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    k = round( randu()*10.0 );
    lambda = ( randu()*10.0 ) + EPS;
    v = kurtosis( k, lambda );
    console.log( 'k: %d, λ: %d, Kurt(X;k,λ): %d', k.toFixed( 4 ), lambda.toFixed( 4 ), 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

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