@stdlib/stats/base/dists/invgamma/kurtosis/lib/main.js

Standard library statistical functions.

/**
* @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' );


// MAIN //

/**
* Returns the excess kurtosis of an inverse gamma distribution.
*
* @param {PositiveNumber} alpha - shape parameter
* @param {PositiveNumber} beta - rate parameter
* @returns {PositiveNumber} kurtosis
*
* @example
* var v = kurtosis( 6.0, 1.0 );
* // returns 19.0
*
* @example
* var v = kurtosis( 5.0, 12.0 );
* // returns 42.0
*
* @example
* var v = kurtosis( 8.0, 2.0 );
* // returns ~8.7
*
* @example
* var v = kurtosis( 5.0, -0.1 );
* // returns NaN
*
* @example
* var v = kurtosis( 6.0, -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 ) {
	if (
		isnan( alpha ) ||
		isnan( beta ) ||
		alpha <= 4.0 ||
		beta <= 0.0
	) {
		return NaN;
	}
	return ( ( 30.0*alpha ) - 66.0 ) / ( ( alpha-3.0 ) * ( alpha-4.0 ) );
}


// EXPORTS //

module.exports = kurtosis;