time-to-botec

Benchmark sampling in different programming languages
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cdf.js (2041B)

      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 
     26 
     27 // MAIN //
     28 
     29 /**
     30 * Evaluates the cumulative distribution function (CDF) for an inverse gamma distribution with shape parameter `alpha` and scale parameter `beta` at a value `x`.
     31 *
     32 * @param {number} x - input value
     33 * @param {PositiveNumber} alpha - shape parameter
     34 * @param {PositiveNumber} beta - scale parameter
     35 * @returns {Probability} evaluated CDF
     36 *
     37 * @example
     38 * var y = cdf( 2.0, 1.0, 1.0 );
     39 * // returns ~0.607
     40 *
     41 * @example
     42 * var y = cdf( 2.0, 3.0, 1.0 );
     43 * // returns ~0.986
     44 *
     45 * @example
     46 * var y = cdf( -1.0, 2.0, 2.0 );
     47 * // returns 0.0
     48 *
     49 * @example
     50 * var y = cdf( +Infinity, 4.0, 2.0 );
     51 * // returns 1.0
     52 *
     53 * @example
     54 * var y = cdf( -Infinity, 4.0, 2.0 );
     55 * // returns 0.0
     56 *
     57 * @example
     58 * var y = cdf( NaN, 0.0, 1.0 );
     59 * // returns NaN
     60 *
     61 * @example
     62 * var y = cdf( 0.0, NaN, 1.0 );
     63 * // returns NaN
     64 *
     65 * @example
     66 * var y = cdf( 0.0, 0.0, NaN );
     67 * // returns NaN
     68 *
     69 * @example
     70 * var y = cdf( 2.0, -1.0, 1.0 );
     71 * // returns NaN
     72 *
     73 * @example
     74 * var y = cdf( 2.0, 1.0, -1.0 );
     75 * // returns NaN
     76 */
     77 function cdf( x, alpha, beta ) {
     78 	if (
     79 		isnan( x ) ||
     80 		isnan( alpha ) ||
     81 		isnan( beta ) ||
     82 		alpha <= 0.0 ||
     83 		beta <= 0.0
     84 	) {
     85 		return NaN;
     86 	}
     87 	if ( x <= 0.0 ) {
     88 		return 0.0;
     89 	}
     90 	return gammainc( beta / x, alpha, true, true );
     91 }
     92 
     93 
     94 // EXPORTS //
     95 
     96 module.exports = cdf;