kurtosis.js (1653B)
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 pow = require( '@stdlib/math/base/special/pow' ); 25 var PI_SQUARED = require( '@stdlib/constants/float64/pi-squared' ); 26 27 28 // MAIN // 29 30 /** 31 * Returns the excess kurtosis for a raised cosine distribution with location `mu` and scale `s`. 32 * 33 * @param {number} mu - location parameter 34 * @param {PositiveNumber} s - scale parameter 35 * @returns {number} excess kurtosis 36 * 37 * @example 38 * var y = kurtosis( 0.0, 1.0 ); 39 * // returns ~-0.594 40 * 41 * @example 42 * var y = kurtosis( 5.0, 2.0 ); 43 * // returns ~-0.594 44 * 45 * @example 46 * var y = kurtosis( NaN, 1.0 ); 47 * // returns NaN 48 * 49 * @example 50 * var y = kurtosis( 0.0, NaN ); 51 * // returns NaN 52 * 53 * @example 54 * var y = kurtosis( 0.0, 0.0 ); 55 * // returns NaN 56 */ 57 function kurtosis( mu, s ) { 58 var out; 59 if ( 60 isnan( mu ) || 61 isnan( s ) || 62 s <= 0.0 63 ) { 64 return NaN; 65 } 66 out = 6.0 * ( 90.0 - ( PI_SQUARED*PI_SQUARED ) ); 67 out /= 5.0 * pow( PI_SQUARED-6.0, 2.0 ); 68 return out; 69 } 70 71 72 // EXPORTS // 73 74 module.exports = kurtosis;