time-to-botec

Benchmark sampling in different programming languages
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kurtosis.js (1975B)

      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 beta = require( '@stdlib/math/base/special/beta' );
     25 
     26 
     27 // MAIN //
     28 
     29 /**
     30 * Returns the excess kurtosis of a Kumaraswamy's double bounded distribution.
     31 *
     32 * @param {PositiveNumber} a - first shape parameter
     33 * @param {PositiveNumber} b - second shape parameter
     34 * @returns {number} excess kurtosis
     35 *
     36 * @example
     37 * var v = kurtosis( 0.5, 1.0 );
     38 * // returns ~2.143
     39 *
     40 * @example
     41 * var v = kurtosis( 4.0, 12.0 );
     42 * // returns ~2.704
     43 *
     44 * @example
     45 * var v = kurtosis( 12.0, 2.0 );
     46 * // returns ~4.817
     47 *
     48 * @example
     49 * var v = kurtosis( 1.0, -0.1 );
     50 * // returns NaN
     51 *
     52 * @example
     53 * var v = kurtosis( -0.1, 1.0 );
     54 * // returns NaN
     55 *
     56 * @example
     57 * var v = kurtosis( 2.0, NaN );
     58 * // returns NaN
     59 *
     60 * @example
     61 * var v = kurtosis( NaN, 2.0 );
     62 * // returns NaN
     63 */
     64 function kurtosis( a, b ) {
     65 	var sigma2;
     66 	var out;
     67 	var mu2;
     68 	var m1;
     69 	var m2;
     70 	var m3;
     71 	var m4;
     72 	if (
     73 		isnan( a ) ||
     74 		a <= 0.0 ||
     75 		isnan( b ) ||
     76 		b <= 0.0
     77 	) {
     78 		return NaN;
     79 	}
     80 	m1 = b * beta( 1.0 + ( 1.0/a ), b );
     81 	m2 = b * beta( 1.0 + ( 2.0/a ), b );
     82 	m3 = b * beta( 1.0 + ( 3.0/a ), b );
     83 	m4 = b * beta( 1.0 + ( 4.0/a ), b );
     84 	sigma2 = m2 - ( m1*m1 );
     85 	mu2 = m1 * m1;
     86 	out = ( m4 - ( 4.0*m3*m1 ) + ( 6.0*m2*mu2 ) - ( 3.0*mu2*mu2 ) );
     87 	out /= sigma2*sigma2;
     88 	return out;
     89 }
     90 
     91 
     92 // EXPORTS //
     93 
     94 module.exports = kurtosis;