time-to-botec

Benchmark sampling in different programming languages
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cdf.js (2146B)

      1 /**
      2 * @license Apache-2.0
      3 *
      4 * Copyright (c) 2020 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 isPositiveInteger = require( '@stdlib/math/base/assert/is-positive-integer' );
     24 var isfinite = require( '@stdlib/math/base/assert/is-finite' );
     25 var isnan = require( '@stdlib/math/base/assert/is-nan' );
     26 var round = require( '@stdlib/math/base/special/round' );
     27 var exp = require( '@stdlib/math/base/special/exp' );
     28 var LN2 = require( '@stdlib/constants/float64/ln-two' );
     29 var weights = require( './weights.js' );
     30 
     31 
     32 // MAIN //
     33 
     34 /**
     35 * Evaluates the cumulative distribution function (CDF) of the Wilcoxon signed rank test statistic with `n` observations.
     36 *
     37 * @param {number} x - input value
     38 * @param {PositiveInteger} n - number of observations
     39 * @returns {Probability} evaluated CDF
     40 *
     41 * @example
     42 * var y = cdf( 7.0, 9 );
     43 * // returns ~0.037
     44 *
     45 * @example
     46 * var y = cdf( 7.0, 6 );
     47 * // returns ~0.281
     48 *
     49 * @example
     50 * var y = cdf( -1.0, 40 );
     51 * // returns 0.0
     52 *
     53 * @example
     54 * var y = cdf( NaN, 10 );
     55 * // returns NaN
     56 *
     57 * @example
     58 * var y = cdf( 0.0, NaN );
     59 * // returns NaN
     60 *
     61 * @example
     62 * var y = cdf( 2.0, -1 );
     63 * // returns NaN
     64 *
     65 * @example
     66 * var y = cdf( 2.0, 1.8 );
     67 * // returns NaN
     68 */
     69 function cdf( x, n ) {
     70 	var mlim;
     71 	var pui;
     72 	var i;
     73 	var p;
     74 	if (
     75 		isnan( x ) ||
     76 		!isPositiveInteger( n ) ||
     77 		!isfinite( n )
     78 	) {
     79 		return NaN;
     80 	}
     81 	if ( x < 0.0 ) {
     82 		return 0.0;
     83 	}
     84 	x = round( x );
     85 	mlim = n * ( n + 1 ) / 2;
     86 	if ( x >= mlim ) {
     87 		return 1.0;
     88 	}
     89 	pui = exp( -n * LN2 );
     90 	p = 0;
     91 	for ( i = 0; i <= x; i++ ) {
     92 		p += weights( i, n ) * pui;
     93 	}
     94 	return p;
     95 }
     96 
     97 
     98 // EXPORTS //
     99 
    100 module.exports = cdf;