time-to-botec

Benchmark sampling in different programming languages
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mgf.js (1839B)

      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 exp = require( '@stdlib/math/base/special/exp' );
     26 
     27 
     28 // MAIN //
     29 
     30 /**
     31 * Evaluates the moment-generating function (MGF) for a Gumbel distribution with location parameter `mu` and scale parameter `b` at a value `t`.
     32 *
     33 * @param {number} t - input value
     34 * @param {number} mu - mean
     35 * @param {PositiveNumber} beta - scale parameter
     36 * @returns {number} evaluated MGF
     37 *
     38 * @example
     39 * var y = mgf( -1.0, 0.0, 3.0 );
     40 * // returns 6.0
     41 *
     42 * @example
     43 * var y = mgf( 0.1, 0.0, 3.0 );
     44 * // returns ~1.298
     45 *
     46 * @example
     47 * var y = mgf( 0.0, 0.0, 1.0 );
     48 * // returns 1.0
     49 *
     50 * @example
     51 * var y = mgf( NaN, 0.0, 1.0 );
     52 * // returns NaN
     53 *
     54 * @example
     55 * var y = mgf( 0.0, NaN, 1.0 );
     56 * // returns NaN
     57 *
     58 * @example
     59 * var y = mgf( 0.0, 0.0, NaN );
     60 * // returns NaN
     61 *
     62 * @example
     63 * // Non-positive scale parameter:
     64 * var y = mgf( 0.0, 0.0, -1.0 );
     65 * // returns NaN
     66 */
     67 function mgf( t, mu, beta ) {
     68 	if (
     69 		isnan( t ) ||
     70 		isnan( mu ) ||
     71 		isnan( beta ) ||
     72 		beta <= 0.0 ||
     73 		t >= 1.0/beta
     74 	) {
     75 		return NaN;
     76 	}
     77 	return gamma( 1.0 - (beta * t) ) * exp( mu * t );
     78 }
     79 
     80 
     81 // EXPORTS //
     82 
     83 module.exports = mgf;