kurtosis.js (1665B)
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 // MAIN // 22 23 /** 24 * Returns the excess kurtosis of a beta distribution. 25 * 26 * @param {PositiveNumber} alpha - first shape parameter 27 * @param {PositiveNumber} beta - second shape parameter 28 * @returns {number} excess kurtosis 29 * 30 * @example 31 * var v = kurtosis( 1.0, 1.0 ); 32 * // returns -1.2 33 * 34 * @example 35 * var v = kurtosis( 4.0, 12.0 ); 36 * // returns ~0.082 37 * 38 * @example 39 * var v = kurtosis( 8.0, 2.0 ); 40 * // returns ~0.49 41 * 42 * @example 43 * var v = kurtosis( 1.0, -0.1 ); 44 * // returns NaN 45 * 46 * @example 47 * var v = kurtosis( -0.1, 1.0 ); 48 * // returns NaN 49 * 50 * @example 51 * var v = kurtosis( 2.0, NaN ); 52 * // returns NaN 53 * 54 * @example 55 * var v = kurtosis( NaN, 2.0 ); 56 * // returns NaN 57 */ 58 function kurtosis( alpha, beta ) { 59 var axb; 60 var amb; 61 var apb; 62 var out; 63 64 if ( alpha <= 0.0 || beta <= 0.0 ) { 65 return NaN; 66 } 67 axb = alpha * beta; 68 amb = alpha - beta; 69 apb = alpha + beta; 70 out = amb * amb * ( apb+1.0 ); 71 out -= axb * ( apb+2.0 ); 72 out *= 6.0; 73 out /= axb * ( apb+2.0 ) * ( apb+3.0 ); 74 return out; 75 } 76 77 78 // EXPORTS // 79 80 module.exports = kurtosis;