skewness.js (1604B)
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 variance = require( './../../../../../base/dists/chi/variance' ); 25 var mean = require( './../../../../../base/dists/chi/mean' ); 26 var sqrt = require( '@stdlib/math/base/special/sqrt' ); 27 28 29 // MAIN // 30 31 /** 32 * Returns the skewness of a chi distribution. 33 * 34 * @param {PositiveNumber} k - degrees of freedom 35 * @returns {PositiveNumber} skewness 36 * 37 * @example 38 * var v = skewness( 9.0 ); 39 * // returns ~0.252 40 * 41 * @example 42 * var v = skewness( 1.0 ); 43 * // returns ~0.995 44 * 45 * @example 46 * var v = skewness( -0.2 ); 47 * // returns NaN 48 * 49 * @example 50 * var v = skewness( NaN ); 51 * // returns NaN 52 */ 53 function skewness( k ) { 54 var sigma3; 55 var sigma2; 56 var sigma; 57 var mu; 58 if ( isnan( k ) || k <= 0.0 ) { 59 return NaN; 60 } 61 mu = mean( k ); 62 sigma = sqrt( variance( k ) ); 63 sigma2 = sigma * sigma; 64 sigma3 = sigma2 * sigma; 65 return ( mu / sigma3 ) * ( 1.0 - ( 2.0*sigma2 ) ); 66 } 67 68 69 // EXPORTS // 70 71 module.exports = skewness;