@stdlib/stats-base-dists-pareto-type1-kurtosis/lib/main.js

Pareto (Type I) distribution excess kurtosis.

/**
* @license Apache-2.0
*
* Copyright (c) 2018 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
*    http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/

'use strict';

// MODULES //

var isnan = require( '@stdlib/math-base-assert-is-nan' );
var pow = require( '@stdlib/math-base-special-pow' );


// MAIN //

/**
* Returns the excess kurtosis of a Pareto (Type I) distribution.
*
* @param {PositiveNumber} alpha - shape parameter
* @param {PositiveNumber} beta - scale parameter
* @returns {PositiveNumber} excess kurtosis
*
* @example
* var v = kurtosis( 5.0, 1.0 );
* // returns ~70.8
*
* @example
* var v = kurtosis( 7.0, 12.0 );
* // returns ~24.857
*
* @example
* var v = kurtosis( 8.0, 2.0 );
* // returns ~19.725
*
* @example
* var v = kurtosis( 1.0, -0.1 );
* // returns NaN
*
* @example
* var v = kurtosis( -0.1, 1.0 );
* // returns NaN
*
* @example
* var v = kurtosis( 2.0, NaN );
* // returns NaN
*
* @example
* var v = kurtosis( NaN, 2.0 );
* // returns NaN
*/
function kurtosis( alpha, beta ) {
	var out;
	if (
		isnan( alpha ) ||
		alpha <= 4.0 ||
		isnan( beta ) ||
		beta <= 0.0
	) {
		return NaN;
	}
	out = 6.0 * ( pow( alpha, 3.0 ) + pow( alpha, 2.0 ) - ( 6.0*alpha ) - 2.0 );
	out /= alpha * ( alpha-3.0 ) * ( alpha-4.0 );
	return out;
}


// EXPORTS //

module.exports = kurtosis;