kurtosis.js (1681B)
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 skewness = require( './../../../../../base/dists/chi/skewness' ); 25 var variance = require( './../../../../../base/dists/chi/variance' ); 26 var mean = require( './../../../../../base/dists/chi/mean' ); 27 var sqrt = require( '@stdlib/math/base/special/sqrt' ); 28 29 30 // MAIN // 31 32 /** 33 * Returns the excess kurtosis of a chi distribution. 34 * 35 * @param {PositiveNumber} k - degrees of freedom 36 * @returns {PositiveNumber} excess kurtosis 37 * 38 * @example 39 * var v = kurtosis( 9.0 ); 40 * // returns ~0.011 41 * 42 * @example 43 * var v = kurtosis( 1.0 ); 44 * // returns ~0.869 45 * 46 * @example 47 * var v = kurtosis( -0.2 ); 48 * // returns NaN 49 * 50 * @example 51 * var v = kurtosis( NaN ); 52 * // returns NaN 53 */ 54 function kurtosis( k ) { 55 var sigma2; 56 var sigma; 57 var g1; 58 var mu; 59 if ( isnan( k ) || k <= 0.0 ) { 60 return NaN; 61 } 62 sigma2 = variance( k ); 63 sigma = sqrt( sigma2 ); 64 mu = mean( k ); 65 g1 = skewness( k ); 66 return ( 2.0/sigma2 ) * ( 1.0 - ( mu*sigma*g1 ) - sigma2 ); 67 } 68 69 70 // EXPORTS // 71 72 module.exports = kurtosis;