time-to-botec

Benchmark sampling in different programming languages
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kurtosis.js (1854B)

      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 
     25 
     26 // MAIN //
     27 
     28 /**
     29 * Returns the excess kurtosis of a beta prime distribution.
     30 *
     31 * @param {PositiveNumber} alpha - first shape parameter
     32 * @param {PositiveNumber} beta - second shape parameter
     33 * @returns {number} kurtosis
     34 *
     35 * @example
     36 * var v = kurtosis( 2.0, 6.0 );
     37 * // returns ~26.143
     38 *
     39 * @example
     40 * var v = kurtosis( 4.0, 12.0 );
     41 * // returns ~5.764
     42 *
     43 * @example
     44 * var v = kurtosis( 12.0, 6.0 );
     45 * // returns ~19.49
     46 *
     47 * @example
     48 * var v = kurtosis( 2.0, 4.0 );
     49 * // returns NaN
     50 *
     51 * @example
     52 * var v = kurtosis( 1.0, -0.1 );
     53 * // returns NaN
     54 *
     55 * @example
     56 * var v = kurtosis( -0.1, 1.0 );
     57 * // returns NaN
     58 *
     59 * @example
     60 * var v = kurtosis( 2.0, NaN );
     61 * // returns NaN
     62 *
     63 * @example
     64 * var v = kurtosis( NaN, 2.0 );
     65 * // returns NaN
     66 */
     67 function kurtosis( alpha, beta ) {
     68 	var abm1;
     69 	var bm1;
     70 	var out;
     71 	if (
     72 		isnan( alpha ) ||
     73 		alpha <= 0.0 ||
     74 		isnan( beta ) ||
     75 		beta <= 4.0
     76 	) {
     77 		return NaN;
     78 	}
     79 	abm1 = alpha + beta - 1.0;
     80 	bm1 = beta - 1.0;
     81 	out = ( alpha * abm1 * ( (5.0*beta )-11.0 ) ) + ( ( bm1*bm1 )*( bm1-1.0 ) );
     82 	out *= 6.0;
     83 	out /= alpha * abm1 * ( beta-3.0 ) * ( beta-4.0 );
     84 	return out;
     85 }
     86 
     87 
     88 // EXPORTS //
     89 
     90 module.exports = kurtosis;