time-to-botec

Benchmark sampling in different programming languages
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mgf.js (2219B)

      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 exp = require( '@stdlib/math/base/special/exp' );
     25 var pow = require( '@stdlib/math/base/special/pow' );
     26 
     27 
     28 // MAIN //
     29 
     30 /**
     31 * Evaluates the moment-generating function (MGF) for a triangular distribution with lower limit `a`, upper limit `b`, and mode `c` at a value `t`.
     32 *
     33 * @param {number} t - input value
     34 * @param {number} a - lower limit
     35 * @param {number} b - upper limit
     36 * @param {number} c - mode
     37 * @returns {number} evaluated MGF
     38 *
     39 * @example
     40 * var y = mgf( 0.5, -1.0, 1.0, 0.0 );
     41 * // returns ~1.021
     42 *
     43 * @example
     44 * var y = mgf( 0.5, -1.0, 1.0, 0.5 );
     45 * // returns ~1.111
     46 *
     47 * @example
     48 * var y = mgf( -0.3, -20.0, 0.0, -2.0 );
     49 * // returns ~24.334
     50 *
     51 * @example
     52 * var y = mgf( -2.0, -1.0, 1.0, 0.0 );
     53 * // returns ~1.381
     54 *
     55 * @example
     56 * var y = mgf( NaN, 0.0, 1.0, 0.5 );
     57 * // returns NaN
     58 *
     59 * @example
     60 * var y = mgf( 0.0, NaN, 1.0, 0.5 );
     61 * // returns NaN
     62 *
     63 * @example
     64 * var y = mgf( 0.0, 0.0, NaN, 0.5 );
     65 * // returns NaN
     66 *
     67 * @example
     68 * var y = mgf( 0.5, 1.0, 0.0, NaN );
     69 * // returns NaN
     70 *
     71 * @example
     72 * var y = mgf( 0.5, 1.0, 0.0, 1.5 );
     73 * // returns NaN
     74 */
     75 function mgf( t, a, b, c ) {
     76 	var bmc;
     77 	var bma;
     78 	var cma;
     79 	var ret;
     80 
     81 	if (
     82 		isnan( t ) ||
     83 		isnan( a ) ||
     84 		isnan( b ) ||
     85 		isnan( c ) ||
     86 		a > c ||
     87 		c > b
     88 	) {
     89 		return NaN;
     90 	}
     91 	if ( t === 0.0 ) {
     92 		return 1.0;
     93 	}
     94 	bmc = b - c;
     95 	bma = b - a;
     96 	cma = c - a;
     97 	ret = (bmc * exp( a * t )) - (bma * exp( c * t ));
     98 	ret += cma * exp( b * t );
     99 	ret *= 2.0;
    100 	ret /= bma * cma * bmc * pow( t, 2.0 );
    101 	return ret;
    102 }
    103 
    104 
    105 // EXPORTS //
    106 
    107 module.exports = mgf;