time-to-botec

Benchmark sampling in different programming languages
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mgf.js (2082B)

      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 abs = require( '@stdlib/math/base/special/abs' );
     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 * Evaluates the moment-generating function (MGF) for a Laplace (double exponential) distribution with location parameter `mu` and scale parameter `b` at a value `t`.
     33 *
     34 * @param {number} t - input value
     35 * @param {number} mu - mean
     36 * @param {NonNegativeNumber} b - scale parameter
     37 * @returns {number} evaluated MGF
     38 *
     39 * @example
     40 * var y = mgf( 0.5, 0.0, 1.0 );
     41 * // returns ~1.333
     42 *
     43 * @example
     44 * var y = mgf( 0.0, 0.0, 1.0 );
     45 * // returns 1.0
     46 *
     47 * @example
     48 * var y = mgf( -1.0, 4.0, 0.2 );
     49 * // returns ~0.019
     50 *
     51 * @example
     52 * var y = mgf( NaN, 0.0, 1.0 );
     53 * // returns NaN
     54 *
     55 * @example
     56 * var y = mgf( 0.0, NaN, 1.0 );
     57 * // returns NaN
     58 *
     59 * @example
     60 * var y = mgf( 0.0, 0.0, NaN );
     61 * // returns NaN
     62 *
     63 * @example
     64 * var y = mgf( 1.0, 0.0, 2.0 );
     65 * // returns NaN
     66 *
     67 * @example
     68 * var y = mgf( -0.5, 0.0, 4.0 );
     69 * // returns NaN
     70 *
     71 * @example
     72 * var y = mgf( 2.0, 0.0, 0.0 );
     73 * // returns NaN
     74 *
     75 * @example
     76 * var y = mgf( 2.0, 0.0, -1.0 );
     77 * // returns NaN
     78 */
     79 function mgf( t, mu, b ) {
     80 	var bt;
     81 	if (
     82 		isnan( t ) ||
     83 		isnan( mu ) ||
     84 		isnan( b ) ||
     85 		b <= 0.0 ||
     86 		abs( t ) >= 1.0/b
     87 	) {
     88 		return NaN;
     89 	}
     90 	bt = b * t;
     91 	return exp( mu * t ) / ( 1.0 - pow( bt, 2.0 ) );
     92 }
     93 
     94 
     95 // EXPORTS //
     96 
     97 module.exports = mgf;