Press n or j to go to the next uncovered block, b, p or k for the previous block.
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 | 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x | /**
* @license Apache-2.0
*
* Copyright (c) 2018 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
'use strict';
// MODULES //
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var beta = require( '@stdlib/math/base/special/beta' );
// MAIN //
/**
* Returns the excess kurtosis of a Kumaraswamy's double bounded distribution.
*
* @param {PositiveNumber} a - first shape parameter
* @param {PositiveNumber} b - second shape parameter
* @returns {number} excess kurtosis
*
* @example
* var v = kurtosis( 0.5, 1.0 );
* // returns ~2.143
*
* @example
* var v = kurtosis( 4.0, 12.0 );
* // returns ~2.704
*
* @example
* var v = kurtosis( 12.0, 2.0 );
* // returns ~4.817
*
* @example
* var v = kurtosis( 1.0, -0.1 );
* // returns NaN
*
* @example
* var v = kurtosis( -0.1, 1.0 );
* // returns NaN
*
* @example
* var v = kurtosis( 2.0, NaN );
* // returns NaN
*
* @example
* var v = kurtosis( NaN, 2.0 );
* // returns NaN
*/
function kurtosis( a, b ) {
var sigma2;
var out;
var mu2;
var m1;
var m2;
var m3;
var m4;
if (
isnan( a ) ||
a <= 0.0 ||
isnan( b ) ||
b <= 0.0
) {
return NaN;
}
m1 = b * beta( 1.0 + ( 1.0/a ), b );
m2 = b * beta( 1.0 + ( 2.0/a ), b );
m3 = b * beta( 1.0 + ( 3.0/a ), b );
m4 = b * beta( 1.0 + ( 4.0/a ), b );
sigma2 = m2 - ( m1*m1 );
mu2 = m1 * m1;
out = ( m4 - ( 4.0*m3*m1 ) + ( 6.0*m2*mu2 ) - ( 3.0*mu2*mu2 ) );
out /= sigma2*sigma2;
return out;
}
// EXPORTS //
module.exports = kurtosis;
|