variance.js (1722B)
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 beta = require( '@stdlib/math/base/special/beta' ); 25 26 27 // MAIN // 28 29 /** 30 * Returns the variance of a Kumaraswamy's double bounded distribution. 31 * 32 * @param {PositiveNumber} a - first shape parameter 33 * @param {PositiveNumber} b - second shape parameter 34 * @returns {PositiveNumber} variance 35 * 36 * @example 37 * var v = variance( 0.5, 1.0 ); 38 * // returns ~0.089 39 * 40 * @example 41 * var v = variance( 4.0, 12.0 ); 42 * // returns ~0.017 43 * 44 * @example 45 * var v = variance( 12.0, 2.0 ); 46 * // returns ~0.006 47 * 48 * @example 49 * var v = variance( 1.0, -0.1 ); 50 * // returns NaN 51 * 52 * @example 53 * var v = variance( -0.1, 1.0 ); 54 * // returns NaN 55 * 56 * @example 57 * var v = variance( 2.0, NaN ); 58 * // returns NaN 59 * 60 * @example 61 * var v = variance( NaN, 2.0 ); 62 * // returns NaN 63 */ 64 function variance( a, b ) { 65 var m1; 66 var m2; 67 if ( 68 isnan( a ) || 69 a <= 0.0 || 70 isnan( b ) || 71 b <= 0.0 72 ) { 73 return NaN; 74 } 75 m1 = b * beta( 1.0 + ( 1.0/a ), b ); 76 m2 = b * beta( 1.0 + ( 2.0/a ), b ); 77 return m2 - ( m1*m1 ); 78 } 79 80 81 // EXPORTS // 82 83 module.exports = variance;