kurtosis.js (1483B)
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 PI = require( '@stdlib/constants/float64/pi' ); 25 26 27 // VARIABLES // 28 29 var KURTOSIS = -( ( 6.0*PI*PI ) - ( 24.0*PI ) + 16.0 ) / ( (4.0-PI)*(4.0-PI) ); 30 31 32 // MAIN // 33 34 /** 35 * Returns the excess kurtosis of a Rayleigh distribution. 36 * 37 * @param {NonNegativeNumber} sigma - scale parameter 38 * @returns {NonNegativeNumber} excess kurtosis 39 * 40 * @example 41 * var v = kurtosis( 9.0 ); 42 * // returns ~0.245 43 * 44 * @example 45 * var v = kurtosis( 5.0 ); 46 * // returns ~0.245 47 * 48 * @example 49 * var v = kurtosis( 3.0 ); 50 * // returns ~0.245 51 * 52 * @example 53 * var v = kurtosis( -0.2 ); 54 * // returns NaN 55 * 56 * @example 57 * var v = kurtosis( NaN ); 58 * // returns NaN 59 */ 60 function kurtosis( sigma ) { 61 if ( isnan( sigma ) || sigma < 0.0 ) { 62 return NaN; 63 } 64 return KURTOSIS; 65 } 66 67 68 // EXPORTS // 69 70 module.exports = kurtosis;