kurtosis.js (1654B)
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 isNonNegativeInteger = require( '@stdlib/math/base/assert/is-nonnegative-integer' ); 24 var isnan = require( '@stdlib/math/base/assert/is-nan' ); 25 var PINF = require( '@stdlib/constants/float64/pinf' ); 26 27 28 // MAIN // 29 30 /** 31 * Returns the kurtosis of a binomial distribution. 32 * 33 * @param {NonNegativeInteger} n - number of trials 34 * @param {Probability} p - success probability 35 * @returns {number} excess kurtosis 36 * 37 * @example 38 * var v = kurtosis( 100, 0.1 ); 39 * // returns ~0.051 40 * 41 * @example 42 * var v = kurtosis( 20, 0.5 ); 43 * // returns ~-0.1 44 * 45 * @example 46 * var v = kurtosis( 10.3, 0.5 ); 47 * // returns NaN 48 * 49 * @example 50 * var v = kurtosis( 20, 1.1 ); 51 * // returns NaN 52 * 53 * @example 54 * var v = kurtosis( 20, NaN ); 55 * // returns NaN 56 */ 57 function kurtosis( n, p ) { 58 var pq; 59 if ( 60 isnan( n ) || 61 isnan( p ) || 62 p < 0.0 || 63 p > 1.0 || 64 !isNonNegativeInteger( n ) || 65 n === PINF 66 ) { 67 return NaN; 68 } 69 pq = p * ( 1.0 - p ); 70 return ( 1.0 - ( 6.0 * pq ) ) / ( n * pq ); 71 } 72 73 74 // EXPORTS // 75 76 module.exports = kurtosis;