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 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 | 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 sqrt = require( '@stdlib/math/base/special/sqrt' );
var pow = require( '@stdlib/math/base/special/pow' );
// MAIN //
/**
* Returns an accumulator function which incrementally computes a corrected sample skewness.
*
* ## Method
*
* The algorithm computes the corrected sample skewness using the formula for `G_1` in [Joanes and Gill 1998][@joanes:1998].
*
* ## References
*
* - Joanes, D. N., and C. A. Gill. 1998. "Comparing measures of sample skewness and kurtosis." _Journal of the Royal Statistical Society: Series D (The Statistician)_ 47 (1). Blackwell Publishers Ltd: 183–89. doi:[10.1111/1467-9884.00122][@joanes:1998].
*
* [@joanes:1998]: http://dx.doi.org/10.1111/1467-9884.00122
*
* @returns {Function} accumulator function
*
* @example
* var accumulator = incrskewness();
*
* var skewness = accumulator();
* // returns null
*
* skewness = accumulator( 2.0 );
* // returns null
*
* skewness = accumulator( -5.0 );
* // returns null
*
* skewness = accumulator( -10.0 );
* // returns ~0.492
*
* skewness = accumulator();
* // returns ~0.492
*/
function incrskewness() {
var deltaN;
var delta;
var term1;
var mean;
var tmp;
var g1;
var M2;
var M3;
var N;
deltaN = 0.0;
delta = 0.0;
term1 = 0.0;
mean = 0.0;
M2 = 0.0;
M3 = 0.0;
N = 0;
return accumulator;
/**
* If provided a value, the accumulator function returns an updated corrected sample skewness. If not provided a value, the accumulator function returns the current corrected sample skewness.
*
* @private
* @param {number} [x] - new value
* @returns {(number|null)} corrected sample skewness or null
*/
function accumulator( x ) {
if ( arguments.length === 0 ) {
if ( N < 3 ) {
return ( isnan( M3 ) ) ? NaN : null;
}
// Calculate the population skewness:
g1 = sqrt( N )*M3 / pow( M2, 1.5 );
// Return the corrected sample skewness:
return sqrt( N*(N-1) )*g1 / (N-2);
}
N += 1;
delta = x - mean;
deltaN = delta / N;
term1 = delta * deltaN * (N-1);
tmp = term1 * deltaN * (N-2);
tmp -= 3.0 * deltaN * M2;
M3 += tmp;
M2 += term1;
mean += deltaN;
if ( N < 3 ) {
return ( isnan( M3 ) ) ? NaN : null;
}
// Calculate the population skewness:
g1 = sqrt( N )*M3 / pow( M2, 1.5 );
// Return the corrected sample skewness:
return sqrt( N*(N-1) )*g1 / (N-2);
}
}
// EXPORTS //
module.exports = incrskewness;
|