time-to-botec

Benchmark sampling in different programming languages
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main.js (3074B)

      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 sqrt = require( '@stdlib/math/base/special/sqrt' );
     25 var pow = require( '@stdlib/math/base/special/pow' );
     26 
     27 
     28 // MAIN //
     29 
     30 /**
     31 * Returns an accumulator function which incrementally computes a corrected sample skewness.
     32 *
     33 * ## Method
     34 *
     35 * The algorithm computes the corrected sample skewness using the formula for `G_1` in [Joanes and Gill 1998][@joanes:1998].
     36 *
     37 * ## References
     38 *
     39 * -   Joanes, D. N., and C. A. Gill. 1998. "Comparing measures of sample skewness and kurtosis." _Journal of the Royal Statistical Society: Series D (The Statistician)_ 47 (1). Blackwell Publishers Ltd: 183–89. doi:[10.1111/1467-9884.00122][@joanes:1998].
     40 *
     41 * [@joanes:1998]: http://dx.doi.org/10.1111/1467-9884.00122
     42 *
     43 *
     44 * @returns {Function} accumulator function
     45 *
     46 * @example
     47 * var accumulator = incrskewness();
     48 *
     49 * var skewness = accumulator();
     50 * // returns null
     51 *
     52 * skewness = accumulator( 2.0 );
     53 * // returns null
     54 *
     55 * skewness = accumulator( -5.0 );
     56 * // returns null
     57 *
     58 * skewness = accumulator( -10.0 );
     59 * // returns ~0.492
     60 *
     61 * skewness = accumulator();
     62 * // returns ~0.492
     63 */
     64 function incrskewness() {
     65 	var deltaN;
     66 	var delta;
     67 	var term1;
     68 	var mean;
     69 	var tmp;
     70 	var g1;
     71 	var M2;
     72 	var M3;
     73 	var N;
     74 
     75 	deltaN = 0.0;
     76 	delta = 0.0;
     77 	term1 = 0.0;
     78 	mean = 0.0;
     79 	M2 = 0.0;
     80 	M3 = 0.0;
     81 	N = 0;
     82 
     83 	return accumulator;
     84 
     85 	/**
     86 	* If provided a value, the accumulator function returns an updated corrected sample skewness. If not provided a value, the accumulator function returns the current corrected sample skewness.
     87 	*
     88 	* @private
     89 	* @param {number} [x] - new value
     90 	* @returns {(number|null)} corrected sample skewness or null
     91 	*/
     92 	function accumulator( x ) {
     93 		if ( arguments.length === 0 ) {
     94 			if ( N < 3 ) {
     95 				return ( isnan( M3 ) ) ? NaN : null;
     96 			}
     97 			// Calculate the population skewness:
     98 			g1 = sqrt( N )*M3 / pow( M2, 1.5 );
     99 
    100 			// Return the corrected sample skewness:
    101 			return sqrt( N*(N-1) )*g1 / (N-2);
    102 		}
    103 		N += 1;
    104 		delta = x - mean;
    105 		deltaN = delta / N;
    106 		term1 = delta * deltaN * (N-1);
    107 
    108 		tmp = term1 * deltaN * (N-2);
    109 		tmp -= 3.0 * deltaN * M2;
    110 		M3 += tmp;
    111 
    112 		M2 += term1;
    113 		mean += deltaN;
    114 		if ( N < 3 ) {
    115 			return ( isnan( M3 ) ) ? NaN : null;
    116 		}
    117 		// Calculate the population skewness:
    118 		g1 = sqrt( N )*M3 / pow( M2, 1.5 );
    119 
    120 		// Return the corrected sample skewness:
    121 		return sqrt( N*(N-1) )*g1 / (N-2);
    122 	}
    123 }
    124 
    125 
    126 // EXPORTS //
    127 
    128 module.exports = incrskewness;