factory.js (2006B)
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 erf = require( '@stdlib/math/base/special/erf' ); 27 var SQRT_HALF_PI = require( '@stdlib/constants/float64/sqrt-half-pi' ); 28 var SQRT2 = require( '@stdlib/constants/float64/sqrt-two' ); 29 30 31 // MAIN // 32 33 /** 34 * Returns a function for evaluating the moment-generating function (MGF) of a Rayleigh distribution with scale parameter `sigma`. 35 * 36 * @param {NonNegativeNumber} sigma - scale parameter 37 * @returns {Function} MGF 38 * 39 * @example 40 * var mgf = factory( 0.5 ); 41 * var y = mgf( 1.0 ); 42 * // returns ~2.715 43 * 44 * y = mgf( 0.5 ); 45 * // returns ~1.888 46 */ 47 function factory( sigma ) { 48 if ( isnan( sigma ) || sigma < 0.0 ) { 49 return constantFunction( NaN ); 50 } 51 return mgf; 52 53 /** 54 * Evaluates the moment-generating function (MGF) for a Rayleigh distribution. 55 * 56 * @private 57 * @param {number} t - input value 58 * @returns {number} evaluated MGF 59 * 60 * @example 61 * var y = mgf( 0.5 ); 62 * // returns <number> 63 */ 64 function mgf( t ) { 65 var sigmat; 66 var ret; 67 68 if ( isnan( t ) ) { 69 return NaN; 70 } 71 sigmat = t * sigma; 72 ret = 1.0 + (sigmat * exp( sigmat*sigmat / 2.0 )); 73 ret *= SQRT_HALF_PI * ( erf( sigmat / SQRT2 ) + 1.0 ); 74 return ret; 75 } 76 } 77 78 79 // EXPORTS // 80 81 module.exports = factory;