time-to-botec

Benchmark sampling in different programming languages
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cdf.js (1971B)

      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 erfc = require( '@stdlib/math/base/special/erfc' );
     24 var sqrt = require( '@stdlib/math/base/special/sqrt' );
     25 var isnan = require( '@stdlib/math/base/assert/is-nan' );
     26 
     27 
     28 // MAIN //
     29 
     30 /**
     31 * Evaluates the cumulative distribution function (CDF) for a Normal distribution with mean `mu` and standard deviation `sigma` at a value `x`.
     32 *
     33 * @param {number} x - input value
     34 * @param {number} mu - mean
     35 * @param {NonNegativeNumber} sigma - standard deviation
     36 * @returns {Probability} evaluated cumulative distribution function
     37 *
     38 * @example
     39 * var y = cdf( 2.0, 0.0, 1.0 );
     40 * // returns ~0.977
     41 *
     42 * @example
     43 * var y = cdf( -1.0, -1.0, 2.0 );
     44 * // returns 0.5
     45 *
     46 * @example
     47 * var y = cdf( -1.0, 4.0, 2.0 );
     48 * // returns ~0.006
     49 *
     50 * @example
     51 * var y = cdf( NaN, 0.0, 1.0 );
     52 * // returns NaN
     53 *
     54 * @example
     55 * var y = cdf( 0.0, NaN, 1.0 );
     56 * // returns NaN
     57 *
     58 * @example
     59 * var y = cdf( 0.0, 0.0, NaN );
     60 * // returns NaN
     61 *
     62 * @example
     63 * // Negative standard deviation:
     64 * var y = cdf( 2.0, 0.0, -1.0 );
     65 * // returns NaN
     66 */
     67 function cdf( x, mu, sigma ) {
     68 	var denom;
     69 	var xc;
     70 	if (
     71 		isnan( x ) ||
     72 		isnan( mu ) ||
     73 		isnan( sigma ) ||
     74 		sigma < 0.0
     75 	) {
     76 		return NaN;
     77 	}
     78 	if ( sigma === 0.0 ) {
     79 		return (x < mu) ? 0.0 : 1.0;
     80 	}
     81 	denom = sigma * sqrt( 2.0 );
     82 	xc = x - mu;
     83 	return 0.5 * erfc( -xc/denom );
     84 }
     85 
     86 
     87 // EXPORTS //
     88 
     89 module.exports = cdf;