time-to-botec

Benchmark sampling in different programming languages
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mgf.js (2154B)

      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 EPS = require( '@stdlib/constants/float64/eps' );
     26 
     27 
     28 // MAIN //
     29 
     30 /**
     31 * Evaluates the moment-generating function (MGF) for a Weibull distribution with shape `k` and scale `lambda` at a value `t`.
     32 *
     33 * @param {number} t - input value
     34 * @param {PositiveNumber} k - shape parameter
     35 * @param {PositiveNumber} lambda - scale parameter
     36 * @returns {number} evaluated MGF
     37 *
     38 * @example
     39 * var y = mgf( 1.0, 1.0, 0.5 );
     40 * // returns ~2.0
     41 *
     42 * @example
     43 * var y = mgf( -1.0, 4.0, 4.0 );
     44 * // returns ~0.019
     45 *
     46 * @example
     47 * var y = mgf( NaN, 1.0, 1.0 );
     48 * // returns NaN
     49 *
     50 * @example
     51 * var y = mgf( 0.0, NaN, 1.0 );
     52 * // returns NaN
     53 *
     54 * @example
     55 * var y = mgf( 0.0, 1.0, NaN );
     56 * // returns NaN
     57 *
     58 * @example
     59 * var y = mgf( 0.2, -1.0, 0.5 );
     60 * // returns NaN
     61 *
     62 * @example
     63 * var y = mgf( 0.2, 0.0, 0.5 );
     64 * // returns NaN
     65 *
     66 * @example
     67 * var y = mgf( 0.2, 0.5, -1.0 );
     68 * // returns NaN
     69 *
     70 * @example
     71 * var y = mgf( 0.2, 0.5, 0.0 );
     72 * // returns NaN
     73 */
     74 function mgf( t, k, lambda ) {
     75 	var summand;
     76 	var sum;
     77 	var c;
     78 	var n;
     79 
     80 	if (
     81 		isnan( t ) ||
     82 		isnan( k ) ||
     83 		isnan( lambda ) ||
     84 		k <= 0.0 ||
     85 		lambda <= 0.0
     86 	) {
     87 		return NaN;
     88 	}
     89 	sum = 1.0;
     90 	c = 1.0;
     91 	n = 0;
     92 	do {
     93 		n += 1;
     94 		c *= ( t * lambda ) / n;
     95 		if ( c === 0.0 ) {
     96 			summand = 0.0;
     97 		} else {
     98 			summand = c * gamma( 1.0 + (n / k) );
     99 		}
    100 		sum += summand;
    101 	} while ( summand / sum > EPS );
    102 	return sum;
    103 }
    104 
    105 
    106 // EXPORTS //
    107 
    108 module.exports = mgf;