mgf.js (1876B)
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 exp = require( '@stdlib/math/base/special/exp' ); 25 26 27 // MAIN // 28 29 /** 30 * Evaluates the moment-generating function (MGF) of a uniform distribution with minimum support `a` and maximum support `b` at a value `t`. 31 * 32 * @param {number} t - input value 33 * @param {number} a - minimum support 34 * @param {number} b - maximum support 35 * @returns {number} evaluated MGF 36 * 37 * @example 38 * var y = mgf( 2.0, 0.0, 4.0 ); 39 * // returns ~372.495 40 * 41 * @example 42 * var y = mgf( -0.2, 0.0, 4.0 ); 43 * // returns ~0.688 44 * 45 * @example 46 * var y = mgf( 2.0, 0.0, 1.0 ); 47 * // returns ~3.195 48 * 49 * @example 50 * var y = mgf( 0.5, 3.0, 2.0 ); 51 * // returns NaN 52 * 53 * @example 54 * var y = mgf( 0.5, 3.0, 3.0 ); 55 * // returns NaN 56 * 57 * @example 58 * var y = mgf( NaN, 0.0, 1.0 ); 59 * // returns NaN 60 * 61 * @example 62 * var y = mgf( 0.0, NaN, 1.0 ); 63 * // returns NaN 64 * 65 * @example 66 * var y = mgf( 0.0, 0.0, NaN ); 67 * // returns NaN 68 */ 69 function mgf( t, a, b ) { 70 var ret; 71 if ( 72 isnan( t ) || 73 isnan( a ) || 74 isnan( b ) || 75 a >= b 76 ) { 77 return NaN; 78 } 79 if ( t === 0.0 ) { 80 return 1.0; 81 } 82 // Case: t not equal to zero 83 ret = exp( t * b ) - exp( t * a ); 84 ret /= t * ( b - a ); 85 return ret; 86 } 87 88 89 // EXPORTS // 90 91 module.exports = mgf;