time-to-botec

Benchmark sampling in different programming languages
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mgf.js (2080B)

      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 var ln = require( '@stdlib/math/base/special/ln' );
     27 
     28 
     29 // MAIN //
     30 
     31 /**
     32 * Evaluates the moment-generating function (MGF) for a negative binomial distribution.
     33 *
     34 * @param {number} t - input value
     35 * @param {PositiveNumber} r - number of successes until experiment is stopped
     36 * @param {Probability} p - success probability
     37 * @returns {number} evaluated MGF
     38 *
     39 * @example
     40 * var y = mgf( 0.05, 20.0, 0.8 );
     41 * // returns ~267.839
     42 *
     43 * @example
     44 * var y = mgf( 0.1, 20.0, 0.1 );
     45 * // returns ~9.347
     46 *
     47 * @example
     48 * var y = mgf( 0.5, 10.0, 0.4 );
     49 * // returns ~42822.023
     50 *
     51 * @example
     52 * var y = mgf( 0.1, 0.0, 0.5 );
     53 * // returns NaN
     54 *
     55 * @example
     56 * var y = mgf( 0.1, -2.0, 0.5 );
     57 * // returns NaN
     58 *
     59 * @example
     60 * var y = mgf( NaN, 20.0, 0.5 );
     61 * // returns NaN
     62 *
     63 * @example
     64 * var y = mgf( 0.0, NaN, 0.5 );
     65 * // returns NaN
     66 *
     67 * @example
     68 * var y = mgf( 0.0, 20.0, NaN );
     69 * // returns NaN
     70 *
     71 * @example
     72 * var y = mgf( 0.2, 20, -1.0 );
     73 * // returns NaN
     74 *
     75 * @example
     76 * var y = mgf( 0.2, 20, 1.5 );
     77 * // returns NaN
     78 */
     79 function mgf( t, r, p ) {
     80 	if (
     81 		isnan( t ) ||
     82 		isnan( r ) ||
     83 		isnan( p ) ||
     84 		r <= 0.0 ||
     85 		p < 0.0 ||
     86 		p > 1.0 ||
     87 		t >= -ln( p )
     88 	) {
     89 		return NaN;
     90 	}
     91 	return pow( ( (1.0 - p) * exp( t ) ) / ( 1.0 - (p * exp( t )) ), r );
     92 }
     93 
     94 
     95 // EXPORTS //
     96 
     97 module.exports = mgf;