variance.js (1916B)
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 gamma = require( '@stdlib/math/base/special/gamma' ); 25 var PINF = require( '@stdlib/constants/float64/pinf' ); 26 27 28 // MAIN // 29 30 /** 31 * Returns the variance for a Fréchet distribution with shape `alpha`, scale `s`, and location `m`. 32 * 33 * @param {PositiveNumber} alpha - shape parameter 34 * @param {PositiveNumber} s - scale parameter 35 * @param {number} m - location parameter 36 * @returns {PositiveNumber} variance 37 * 38 * @example 39 * var y = variance( 5.0, 2.0, 0.0 ); 40 * // returns ~0.535 41 * 42 * @example 43 * var y = variance( 5.0, 2.0, -5.0 ); 44 * // returns ~0.535 45 * 46 * @example 47 * var y = variance( 1.0, 1.0, 0.0 ); 48 * // returns Infinity 49 * 50 * @example 51 * var y = variance( NaN, 1.0, 0.0 ); 52 * // returns NaN 53 * 54 * @example 55 * var y = variance( 1.0, NaN, 0.0 ); 56 * // returns NaN 57 * 58 * @example 59 * var y = variance( 1.0, 1.0, NaN ); 60 * // returns NaN 61 */ 62 function variance( alpha, s, m ) { 63 var g1; 64 var g2; 65 if ( 66 isnan( alpha ) || 67 isnan( s ) || 68 isnan( m ) || 69 alpha <= 0.0 || 70 s <= 0.0 71 ) { 72 return NaN; 73 } 74 if ( alpha <= 2.0 ) { 75 // Case: 0 < alpha <= 2 76 return PINF; 77 } 78 g1 = gamma( 1.0 - ( 1.0/alpha ) ); 79 g2 = gamma( 1.0 - ( 2.0/alpha ) ); 80 return ( s*s ) * ( g2 - ( g1*g1 ) ); 81 } 82 83 84 // EXPORTS // 85 86 module.exports = variance;