variance.js (1676B)
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 variance of a discrete uniform distribution. 32 * 33 * @param {integer} a - minimum support 34 * @param {integer} b - maximum support 35 * @returns {PositiveNumber} variance 36 * 37 * @example 38 * var v = variance( 0, 1 ); 39 * // returns ~0.25 40 * 41 * @example 42 * var v = variance( 4, 12 ); 43 * // returns ~6.667 44 * 45 * @example 46 * var v = variance( -4, 4 ); 47 * // returns ~6.667 48 * 49 * @example 50 * var v = variance( 1, -0.1 ); 51 * // returns NaN 52 * 53 * @example 54 * var v = variance( 0.5, 1 ); 55 * // returns NaN 56 * 57 * @example 58 * var v = variance( 2, NaN ); 59 * // returns NaN 60 * 61 * @example 62 * var v = variance( NaN, 2 ); 63 * // returns NaN 64 */ 65 function variance( a, b ) { 66 if ( 67 isnan( a ) || 68 isnan( b ) || 69 !isInteger( a ) || 70 !isInteger( b ) || 71 a > b 72 ) { 73 return NaN; 74 } 75 return ( pow( b-a+1, 2.0 ) - 1.0 ) / 12.0; 76 } 77 78 79 // EXPORTS // 80 81 module.exports = variance;