factory.js (2101B)
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 constantFunction = require( '@stdlib/utils/constant-function' ); 24 var isnan = require( '@stdlib/math/base/assert/is-nan' ); 25 var exp = require( '@stdlib/math/base/special/exp' ); 26 var pow = require( '@stdlib/math/base/special/pow' ); 27 28 29 // MAIN // 30 31 /** 32 * Returns a function for evaluating the moment-generating function (MGF) for a triangular distribution with lower limit `a`, upper limit `b`, and mode `c`. 33 * 34 * @param {number} a - lower limit 35 * @param {number} b - upper limit 36 * @param {number} c - mode 37 * @returns {Function} MGF 38 * 39 * @example 40 * var mgf = factory( 0.0, 2.0, 1.0 ); 41 * var y = mgf( -1.0 ); 42 * // returns ~0.3996 43 * 44 * y = mgf( 2.0 ); 45 * // returns ~10.205 46 */ 47 function factory( a, b, c ) { 48 var bmc; 49 var bma; 50 var cma; 51 52 if ( 53 isnan( a ) || 54 isnan( b ) || 55 isnan( c ) || 56 a > c || 57 c > b 58 ) { 59 return constantFunction( NaN ); 60 } 61 bmc = b - c; 62 bma = b - a; 63 cma = c - a; 64 return mgf; 65 66 /** 67 * Evaluates the moment-generating function (MGF) for a triangular distribution. 68 * 69 * @private 70 * @param {number} t - input value 71 * @returns {number} evaluated MGF 72 * 73 * @example 74 * var y = mgf( 0.5 ); 75 * // returns <number> 76 */ 77 function mgf( t ) { 78 var ret; 79 80 if ( isnan( t ) ) { 81 return NaN; 82 } 83 if ( t === 0.0 ) { 84 return 1.0; 85 } 86 ret = (bmc * exp( a * t )) - (bma * exp( c * t )); 87 ret += cma * exp( b * t ); 88 ret *= 2.0; 89 ret /= bma * cma * bmc * pow( t, 2.0 ); 90 return ret; 91 } 92 } 93 94 95 // EXPORTS // 96 97 module.exports = factory;