kurtosis.js (1682B)
1 /** 2 * @license Apache-2.0 3 * 4 * Copyright (c) 2018 The Stdlib Authors. 5 * 6 * Licensed under the Apache License, Version 2.0 (the "License"); 7 * you may not use this file except in compliance with the License. 8 * You may obtain a copy of the License at 9 * 10 * http://www.apache.org/licenses/LICENSE-2.0 11 * 12 * Unless required by applicable law or agreed to in writing, software 13 * distributed under the License is distributed on an "AS IS" BASIS, 14 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 15 * See the License for the specific language governing permissions and 16 * limitations under the License. 17 */ 18 19 'use strict'; 20 21 // MODULES // 22 23 var isnan = require( '@stdlib/math/base/assert/is-nan' ); 24 25 26 // MAIN // 27 28 /** 29 * Returns the excess kurtosis of an inverse gamma distribution. 30 * 31 * @param {PositiveNumber} alpha - shape parameter 32 * @param {PositiveNumber} beta - rate parameter 33 * @returns {PositiveNumber} kurtosis 34 * 35 * @example 36 * var v = kurtosis( 6.0, 1.0 ); 37 * // returns 19.0 38 * 39 * @example 40 * var v = kurtosis( 5.0, 12.0 ); 41 * // returns 42.0 42 * 43 * @example 44 * var v = kurtosis( 8.0, 2.0 ); 45 * // returns ~8.7 46 * 47 * @example 48 * var v = kurtosis( 5.0, -0.1 ); 49 * // returns NaN 50 * 51 * @example 52 * var v = kurtosis( 6.0, -0.1 ); 53 * // returns NaN 54 * 55 * @example 56 * var v = kurtosis( -0.1, 1.0 ); 57 * // returns NaN 58 * 59 * @example 60 * var v = kurtosis( 2.0, NaN ); 61 * // returns NaN 62 * 63 * @example 64 * var v = kurtosis( NaN, 2.0 ); 65 * // returns NaN 66 */ 67 function kurtosis( alpha, beta ) { 68 if ( 69 isnan( alpha ) || 70 isnan( beta ) || 71 alpha <= 4.0 || 72 beta <= 0.0 73 ) { 74 return NaN; 75 } 76 return ( ( 30.0*alpha ) - 66.0 ) / ( ( alpha-3.0 ) * ( alpha-4.0 ) ); 77 } 78 79 80 // EXPORTS // 81 82 module.exports = kurtosis;