time-to-botec

Benchmark sampling in different programming languages
Log | Files | Refs | README

skewness.js (2096B)

      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 variance = require( './../../../../../base/dists/weibull/variance' );
     25 var gamma = require( '@stdlib/math/base/special/gamma' );
     26 var sqrt = require( '@stdlib/math/base/special/sqrt' );
     27 var mean = require( './../../../../../base/dists/weibull/mean' );
     28 var pow = require( '@stdlib/math/base/special/pow' );
     29 
     30 
     31 // MAIN //
     32 
     33 /**
     34 * Returns the skewness of a Weibull distribution.
     35 *
     36 * @param {PositiveNumber} k - shape parameter
     37 * @param {PositiveNumber} lambda - scale parameter
     38 * @returns {number} skewness
     39 *
     40 * @example
     41 * var v = skewness( 1.0, 1.0 );
     42 * // returns 2.0
     43 *
     44 * @example
     45 * var v = skewness( 4.0, 12.0 );
     46 * // returns ~-0.087
     47 *
     48 * @example
     49 * var v = skewness( 8.0, 2.0 );
     50 * // returns ~-0.534
     51 *
     52 * @example
     53 * var v = skewness( 1.0, -0.1 );
     54 * // returns NaN
     55 *
     56 * @example
     57 * var v = skewness( -0.1, 1.0 );
     58 * // returns NaN
     59 *
     60 * @example
     61 * var v = skewness( 2.0, NaN );
     62 * // returns NaN
     63 *
     64 * @example
     65 * var v = skewness( NaN, 2.0 );
     66 * // returns NaN
     67 */
     68 function skewness( k, lambda ) {
     69 	var sigma2;
     70 	var sigma;
     71 	var out;
     72 	var mu;
     73 	if (
     74 		isnan( k ) ||
     75 		isnan( lambda ) ||
     76 		k <= 0.0 ||
     77 		lambda <= 0.0
     78 	) {
     79 		return NaN;
     80 	}
     81 	mu = mean( k, lambda );
     82 	sigma2 = variance( k, lambda);
     83 	sigma = sqrt( sigma2 );
     84 	out = gamma( 1.0 + ( 3.0/k ) ) * pow( lambda, 3.0 );
     85 	out -= ( 3.0*mu*sigma2 ) + pow( mu, 3.0 );
     86 	out /= pow( sigma, 3.0 );
     87 	return out;
     88 }
     89 
     90 
     91 // EXPORTS //
     92 
     93 module.exports = skewness;