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 | 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) 2025 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 SQRT2 = require( '@stdlib/constants/float64/sqrt-two' );
var sqrt = require( '@stdlib/math/base/special/sqrt' );
var ln = require( '@stdlib/math/base/special/ln' );
// MAIN //
/**
* Returns the skewness of a Bradford distribution.
*
* @param {PositiveNumber} c - shape parameter
* @returns {PositiveNumber} skewness
*
* @example
* var v = skewness( 9.0 );
* // returns ~0.772
*
* @example
* var v = skewness( 1.0 );
* // returns ~0.239
*
* @example
* var v = skewness( -0.2 );
* // returns NaN
*
* @example
* var v = skewness( NaN );
* // returns NaN
*/
function skewness( c ) {
var ans;
var t1;
var t2;
var t3;
var p;
if ( isnan( c ) || c <= 0.0 ) {
return NaN;
}
p = ln( 1.0 + c );
t1 = 12.0 * ( c*c );
t2 = 9.0 * c * p * ( c + 2.0 );
t3 = 2.0 * ( p*p ) * ( ( c * ( c + 3.0 ) ) + 3.0 );
ans = SQRT2 * ( t1 - t2 + t3 );
t1 = c * ( ( c * ( p - 2.0 ) ) + ( 2.0 * p ) );
t2 = ( 3.0 * c * ( p - 2.0 ) ) + ( 6.0 * p );
ans /= sqrt( t1 ) * t2;
return ans;
}
// EXPORTS //
module.exports = skewness;
|