time-to-botec

Benchmark sampling in different programming languages
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kurtosis.js (1933B)

      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 gamma = require( '@stdlib/math/base/special/gamma' );
     25 var pow = require( '@stdlib/math/base/special/pow' );
     26 
     27 
     28 // MAIN //
     29 
     30 /**
     31 * Returns the excess kurtosis of a Weibull distribution.
     32 *
     33 * @param {PositiveNumber} k - shape parameter
     34 * @param {PositiveNumber} lambda - scale parameter
     35 * @returns {number} kurtosis
     36 *
     37 * @example
     38 * var v = kurtosis( 1.0, 1.0 );
     39 * // returns 6.0
     40 *
     41 * @example
     42 * var v = kurtosis( 4.0, 12.0 );
     43 * // returns ~-0.252
     44 *
     45 * @example
     46 * var v = kurtosis( 8.0, 2.0 );
     47 * // returns ~0.328
     48 *
     49 * @example
     50 * var v = kurtosis( 1.0, -0.1 );
     51 * // returns NaN
     52 *
     53 * @example
     54 * var v = kurtosis( -0.1, 1.0 );
     55 * // returns NaN
     56 *
     57 * @example
     58 * var v = kurtosis( 2.0, NaN );
     59 * // returns NaN
     60 *
     61 * @example
     62 * var v = kurtosis( NaN, 2.0 );
     63 * // returns NaN
     64 */
     65 function kurtosis( k, lambda ) {
     66 	var out;
     67 	var g4;
     68 	var g3;
     69 	var g2;
     70 	var g1;
     71 	if (
     72 		isnan( k ) ||
     73 		isnan( lambda ) ||
     74 		k <= 0.0 ||
     75 		lambda <= 0.0
     76 	) {
     77 		return NaN;
     78 	}
     79 	g1 = gamma( 1.0 + (1.0/k) );
     80 	g2 = gamma( 1.0 + (2.0/k) );
     81 	g3 = gamma( 1.0 + (3.0/k) );
     82 	g4 = gamma( 1.0 + (4.0/k) );
     83 	out = (-6.0*pow(g1, 4.0)) + (12.0*g1*g1*g2) - (3.0*g2*g2)- (4.0*g1*g3) + g4;
     84 	out /= pow( g2 - (g1*g1), 2.0 );
     85 	return out;
     86 }
     87 
     88 
     89 // EXPORTS //
     90 
     91 module.exports = kurtosis;