kurtosis.js (1721B)
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 isInteger = require( '@stdlib/math/base/assert/is-integer' ); 25 var pow = require( '@stdlib/math/base/special/pow' ); 26 27 28 // MAIN // 29 30 /** 31 * Returns the excess kurtosis of a discrete uniform distribution. 32 * 33 * @param {integer} a - minimum support 34 * @param {integer} b - maximum support 35 * @returns {number} excess kurtosis 36 * 37 * @example 38 * var v = kurtosis( 0, 1 ); 39 * // returns -2.0 40 * 41 * @example 42 * var v = kurtosis( 4, 12 ); 43 * // returns ~-1.23 44 * 45 * @example 46 * var v = kurtosis( -4, 4 ); 47 * // returns ~-1.23 48 * 49 * @example 50 * var v = kurtosis( 1, 0.4 ); 51 * // returns NaN 52 * 53 * @example 54 * var v = kurtosis( -0.1, 1 ); 55 * // returns NaN 56 * 57 * @example 58 * var v = kurtosis( 2, NaN ); 59 * // returns NaN 60 * 61 * @example 62 * var v = kurtosis( NaN, 2 ); 63 * // returns NaN 64 */ 65 function kurtosis( a, b ) { 66 var n2; 67 if ( 68 isnan( a ) || 69 isnan( b ) || 70 !isInteger( a ) || 71 !isInteger( b ) || 72 a > b 73 ) { 74 return NaN; 75 } 76 n2 = pow( b - a + 1.0, 2.0 ); 77 return -1.2 * ( n2 + 1.0 ) / ( n2 - 1.0 ); 78 } 79 80 81 // EXPORTS // 82 83 module.exports = kurtosis;