kurtosis.js (1637B)
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 exp = require( '@stdlib/math/base/special/exp' ); 25 26 27 // MAIN // 28 29 /** 30 * Returns the excess kurtosis for a lognormal distribution with location `mu` and scale `sigma`. 31 * 32 * @param {number} mu - location parameter 33 * @param {PositiveNumber} sigma - scale parameter 34 * @returns {number} excess kurtosis 35 * 36 * @example 37 * var y = kurtosis( 0.0, 1.0 ); 38 * // returns ~110.936 39 * 40 * @example 41 * var y = kurtosis( 5.0, 2.0 ); 42 * // returns ~9220556.977 43 * 44 * @example 45 * var y = kurtosis( NaN, 1.0 ); 46 * // returns NaN 47 * 48 * @example 49 * var y = kurtosis( 0.0, NaN ); 50 * // returns NaN 51 * 52 * @example 53 * var y = kurtosis( 0.0, 0.0 ); 54 * // returns NaN 55 */ 56 function kurtosis( mu, sigma ) { 57 var out; 58 var s2; 59 if ( 60 isnan( mu ) || 61 isnan( sigma ) || 62 sigma <= 0.0 63 ) { 64 return NaN; 65 } 66 s2 = sigma * sigma; 67 out = exp( 4.0*s2 ); 68 out += 2.0 * exp( 3.0*s2 ); 69 out += 3.0 * exp( 2.0*s2 ); 70 out -= 6.0; 71 return out; 72 } 73 74 75 // EXPORTS // 76 77 module.exports = kurtosis;