_mgf.js (1795B)
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 betaFcn = require( '@stdlib/math/base/special/beta' ); 24 var abs = require( '@stdlib/math/base/special/abs' ); 25 var EPS = require( '@stdlib/constants/float64/eps' ); 26 27 28 // MAIN // 29 30 /** 31 * Evaluates the moment-generating function (MGF) for a beta distribution with first shape parameter `alpha` and second shape parameter `beta` at a value `t`. 32 * 33 * @private 34 * @param {number} t - input value 35 * @param {PositiveNumber} alpha - first shape parameter 36 * @param {PositiveNumber} beta - second shape parameter 37 * @returns {number} evaluated MGF 38 * 39 * @example 40 * var y = mgf( 0.5, 1.0, 1.0 ); 41 * // returns ~1.297 42 * 43 * @example 44 * var y = mgf( 0.5, 2.0, 4.0 ); 45 * // returns ~1.186 46 * 47 * @example 48 * var y = mgf( 3.0, 2.0, 2.0 ); 49 * // returns ~5.575 50 * 51 * @example 52 * var y = mgf( -0.8, 4.0, 4.0 ); 53 * // returns ~0.676 54 */ 55 function mgf( t, alpha, beta ) { 56 var summand; 57 var denom; 58 var sum; 59 var c; 60 var k; 61 62 denom = betaFcn( alpha, beta ); 63 sum = 1.0; 64 c = 1.0; 65 k = 1; 66 do { 67 c *= t / k; 68 summand = ( betaFcn( alpha+k, beta ) / denom ) * c; 69 sum += summand; 70 k += 1; 71 } while ( abs( summand / sum ) >= EPS ); 72 return sum; 73 } 74 75 76 // EXPORTS // 77 78 module.exports = mgf;