time-to-botec

Benchmark sampling in different programming languages
Log | Files | Refs | README

mgf.js (2050B)

      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 isInteger = require( '@stdlib/math/base/assert/is-integer' );
     24 var isnan = require( '@stdlib/math/base/assert/is-nan' );
     25 var expm1 = require( '@stdlib/math/base/special/expm1' );
     26 var exp = require( '@stdlib/math/base/special/exp' );
     27 
     28 
     29 // MAIN //
     30 
     31 /**
     32 * Evaluates the moment-generating function (MGF) of a discrete uniform distribution with minimum support `a` and maximum support `b` at a value `t`.
     33 *
     34 * @param {number} t - input value
     35 * @param {integer} a - minimum support
     36 * @param {integer} b - maximum support
     37 * @returns {number} evaluated MGF
     38 *
     39 * @example
     40 * var y = mgf( 2.0, 0, 4 );
     41 * // returns ~689.475
     42 *
     43 * @example
     44 * var y = mgf( -0.2, 0, 4 );
     45 * // returns ~0.697
     46 *
     47 * @example
     48 * var y = mgf( 2.0, 0, 1 );
     49 * // returns ~4.195
     50 *
     51 * @example
     52 * var y = mgf( 0.5, 3, 3 );
     53 * // returns ~4.482
     54 *
     55 * @example
     56 * var y = mgf( 0.5, 3, 2 );
     57 * // returns NaN
     58 *
     59 * @example
     60 * var y = mgf( NaN, 0, 1 );
     61 * // returns NaN
     62 *
     63 * @example
     64 * var y = mgf( 0.0, NaN, 1 );
     65 * // returns NaN
     66 *
     67 * @example
     68 * var y = mgf( 0.0, 0, NaN );
     69 * // returns NaN
     70 */
     71 function mgf( t, a, b ) {
     72 	var ret;
     73 	var n;
     74 	if (
     75 		isnan( t ) ||
     76 		isnan( a ) ||
     77 		isnan( b ) ||
     78 		!isInteger( a ) ||
     79 		!isInteger( b ) ||
     80 		a > b
     81 	) {
     82 		return NaN;
     83 	}
     84 	if ( t === 0.0 ) {
     85 		return 1.0;
     86 	}
     87 	// Case: t not equal to zero
     88 	n = b - a + 1;
     89 	ret = exp( t*a ) * expm1( t*n );
     90 	ret /= n * expm1( t );
     91 	return ret;
     92 }
     93 
     94 
     95 // EXPORTS //
     96 
     97 module.exports = mgf;