time-to-botec

Benchmark sampling in different programming languages
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kurtosis.js (2142B)

      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 var PINF = require( '@stdlib/constants/float64/pinf' );
     27 
     28 
     29 // MAIN //
     30 
     31 /**
     32 * Returns the excess kurtosis for a Fréchet distribution with shape `alpha`, scale `s`, and location `m`.
     33 *
     34 * @param {PositiveNumber} alpha - shape parameter
     35 * @param {PositiveNumber} s - scale parameter
     36 * @param {number} m - location parameter
     37 * @returns {number} excess kurtosis
     38 *
     39 * @example
     40 * var y = kurtosis( 5.0, 2.0, 0.0 );
     41 * // returns ~45.092
     42 *
     43 * @example
     44 * var y = kurtosis( 5.0, 2.0, -5.0 );
     45 * // returns ~45.092
     46 *
     47 * @example
     48 * var y = kurtosis( 3.8, 1.0, 0.0 );
     49 * // returns Infinity
     50 *
     51 * @example
     52 * var y = kurtosis( NaN, 1.0, 0.0 );
     53 * // returns NaN
     54 *
     55 * @example
     56 * var y = kurtosis( 1.0, NaN, 0.0 );
     57 * // returns NaN
     58 *
     59 * @example
     60 * var y = kurtosis( 1.0, 1.0, NaN );
     61 * // returns NaN
     62 */
     63 function kurtosis( alpha, s, m ) {
     64 	var out;
     65 	var g1;
     66 	var g2;
     67 	var g3;
     68 	var g4;
     69 	if (
     70 		isnan( alpha ) ||
     71 		isnan( s ) ||
     72 		isnan( m ) ||
     73 		alpha <= 0.0 ||
     74 		s <= 0.0
     75 	) {
     76 		return NaN;
     77 	}
     78 	if ( alpha <= 4.0 ) {
     79 		// Case: 0 < alpha <= 4
     80 		return PINF;
     81 	}
     82 	g1 = gamma( 1.0 - ( 1.0/alpha ) );
     83 	g2 = gamma( 1.0 - ( 2.0/alpha ) );
     84 	g3 = gamma( 1.0 - ( 3.0/alpha ) );
     85 	g4 = gamma( 1.0 - ( 4.0/alpha ) );
     86 	out = ( g4 - ( 4.0*g3*g1 ) + ( 3.0*g2*g2 ) ) / pow( g2 - ( g1*g1 ), 2.0 );
     87 	out -= 6.0;
     88 	return out;
     89 }
     90 
     91 
     92 // EXPORTS //
     93 
     94 module.exports = kurtosis;