variance.js (1712B)
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 25 26 // MAIN // 27 28 /** 29 * Returns the variance of a beta prime distribution. 30 * 31 * @param {PositiveNumber} alpha - first shape parameter 32 * @param {PositiveNumber} beta - second shape parameter 33 * @returns {PositiveNumber} variance 34 * 35 * @example 36 * var v = variance( 1.0, 3.0 ); 37 * // returns ~0.75 38 * 39 * @example 40 * var v = variance( 4.0, 12.0 ); 41 * // returns ~0.05 42 * 43 * @example 44 * var v = variance( 8.0, 2.5 ); 45 * // returns ~67.556 46 * 47 * @example 48 * var v = variance( 8.0, 2.0 ); 49 * // returns NaN 50 * 51 * @example 52 * var v = variance( 1.0, -0.1 ); 53 * // returns NaN 54 * 55 * @example 56 * var v = variance( -0.1, 1.0 ); 57 * // returns NaN 58 * 59 * @example 60 * var v = variance( 2.0, NaN ); 61 * // returns NaN 62 * 63 * @example 64 * var v = variance( NaN, 2.0 ); 65 * // returns NaN 66 */ 67 function variance( alpha, beta ) { 68 var bm1; 69 if ( 70 isnan( alpha ) || 71 alpha <= 0.0 || 72 isnan( beta ) || 73 beta <= 2.0 74 ) { 75 return NaN; 76 } 77 bm1 = beta - 1.0; 78 return ( alpha * ( alpha + bm1 ) ) / ( ( bm1-1.0 ) * bm1*bm1 ); 79 } 80 81 82 // EXPORTS // 83 84 module.exports = variance;