skewness.js (1902B)
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 var beta = require( '@stdlib/math/base/special/beta' ); 25 var pow = require( '@stdlib/math/base/special/pow' ); 26 27 28 // MAIN // 29 30 /** 31 * Returns the skewness of a Kumaraswamy's double bounded distribution. 32 * 33 * @param {PositiveNumber} a - first shape parameter 34 * @param {PositiveNumber} b - second shape parameter 35 * @returns {number} skewness 36 * 37 * @example 38 * var v = skewness( 0.5, 1.0 ); 39 * // returns ~0.639 40 * 41 * @example 42 * var v = skewness( 4.0, 12.0 ); 43 * // returns ~-0.201 44 * 45 * @example 46 * var v = skewness( 12.0, 2.0 ); 47 * // returns ~-1.2 48 * 49 * @example 50 * var v = skewness( 1.0, -0.1 ); 51 * // returns NaN 52 * 53 * @example 54 * var v = skewness( -0.1, 1.0 ); 55 * // returns NaN 56 * 57 * @example 58 * var v = skewness( 2.0, NaN ); 59 * // returns NaN 60 * 61 * @example 62 * var v = skewness( NaN, 2.0 ); 63 * // returns NaN 64 */ 65 function skewness( a, b ) { 66 var sigma2; 67 var m1; 68 var m2; 69 var m3; 70 if ( 71 isnan( a ) || 72 a <= 0.0 || 73 isnan( b ) || 74 b <= 0.0 75 ) { 76 return NaN; 77 } 78 m1 = b * beta( 1.0 + ( 1.0/a ), b ); 79 m2 = b * beta( 1.0 + ( 2.0/a ), b ); 80 m3 = b * beta( 1.0 + ( 3.0/a ), b ); 81 sigma2 = m2 - ( m1*m1 ); 82 return ( m3 - ( 3.0*m1*sigma2 ) - ( m1*m1*m1 ) ) / pow( sigma2, 1.5 ); 83 } 84 85 86 // EXPORTS // 87 88 module.exports = skewness;