time-to-botec

Benchmark sampling in different programming languages
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cdf.js (2173B)

      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 gammainc = require( '@stdlib/math/base/special/gammainc' );
     24 var isnan = require( '@stdlib/math/base/assert/is-nan' );
     25 var PINF = require( '@stdlib/constants/float64/pinf' );
     26 
     27 
     28 // MAIN //
     29 
     30 /**
     31 * Evaluates the cumulative distribution function (CDF) for a gamma distribution with shape parameter `alpha` and rate parameter `beta` at a value `x`.
     32 *
     33 * @param {number} x - input value
     34 * @param {NonNegativeNumber} alpha - shape parameter
     35 * @param {PositiveNumber} beta - rate parameter
     36 * @returns {Probability} evaluated CDF
     37 *
     38 * @example
     39 * var y = cdf( 2.0, 1.0, 1.0 );
     40 * // returns ~0.865
     41 *
     42 * @example
     43 * var y = cdf( 2.0, 3.0, 1.0 );
     44 * // returns ~0.323
     45 *
     46 * @example
     47 * var y = cdf( -1.0, 2.0, 2.0 );
     48 * // returns 0.0
     49 *
     50 * @example
     51 * var y = cdf( +Infinity, 4.0, 2.0 );
     52 * // returns 1.0
     53 *
     54 * @example
     55 * var y = cdf( -Infinity, 4.0, 2.0 );
     56 * // returns 0.0
     57 *
     58 * @example
     59 * var y = cdf( NaN, 0.0, 1.0 );
     60 * // returns NaN
     61 *
     62 * @example
     63 * var y = cdf( 0.0, NaN, 1.0 );
     64 * // returns NaN
     65 *
     66 * @example
     67 * var y = cdf( 0.0, 0.0, NaN );
     68 * // returns NaN
     69 *
     70 * @example
     71 * var y = cdf( 2.0, -1.0, 1.0 );
     72 * // returns NaN
     73 *
     74 * @example
     75 * var y = cdf( 2.0, 1.0, -1.0 );
     76 * // returns NaN
     77 */
     78 function cdf( x, alpha, beta ) {
     79 	if (
     80 		isnan( x ) ||
     81 		isnan( alpha ) ||
     82 		isnan( beta ) ||
     83 		alpha < 0.0 ||
     84 		beta <= 0.0
     85 	) {
     86 		return NaN;
     87 	}
     88 	if ( alpha === 0.0 ) {
     89 		return ( x < 0 ) ? 0.0 : 1.0;
     90 	}
     91 	if ( x <= 0.0 ) {
     92 		return 0.0;
     93 	}
     94 	if ( x === PINF ) {
     95 		return 1.0;
     96 	}
     97 	return gammainc( x * beta, alpha );
     98 }
     99 
    100 
    101 // EXPORTS //
    102 
    103 module.exports = cdf;