129 lines
3.0 KiB
JavaScript
129 lines
3.0 KiB
JavaScript
/**
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* @license Apache-2.0
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*
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* Copyright (c) 2018 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var sqrt = require( '@stdlib/math/base/special/sqrt' );
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var pow = require( '@stdlib/math/base/special/pow' );
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// MAIN //
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/**
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* Returns an accumulator function which incrementally computes a corrected sample skewness.
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*
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* ## Method
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*
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* The algorithm computes the corrected sample skewness using the formula for `G_1` in [Joanes and Gill 1998][@joanes:1998].
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*
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* ## References
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*
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* - 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].
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*
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* [@joanes:1998]: http://dx.doi.org/10.1111/1467-9884.00122
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*
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*
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* @returns {Function} accumulator function
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*
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* @example
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* var accumulator = incrskewness();
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*
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* var skewness = accumulator();
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* // returns null
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*
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* skewness = accumulator( 2.0 );
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* // returns null
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*
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* skewness = accumulator( -5.0 );
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* // returns null
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*
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* skewness = accumulator( -10.0 );
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* // returns ~0.492
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*
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* skewness = accumulator();
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* // returns ~0.492
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*/
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function incrskewness() {
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var deltaN;
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var delta;
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var term1;
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var mean;
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var tmp;
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var g1;
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var M2;
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var M3;
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var N;
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deltaN = 0.0;
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delta = 0.0;
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term1 = 0.0;
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mean = 0.0;
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M2 = 0.0;
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M3 = 0.0;
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N = 0;
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return accumulator;
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/**
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* 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.
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*
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* @private
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* @param {number} [x] - new value
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* @returns {(number|null)} corrected sample skewness or null
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*/
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function accumulator( x ) {
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if ( arguments.length === 0 ) {
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if ( N < 3 ) {
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return ( isnan( M3 ) ) ? NaN : null;
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}
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// Calculate the population skewness:
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g1 = sqrt( N )*M3 / pow( M2, 1.5 );
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// Return the corrected sample skewness:
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return sqrt( N*(N-1) )*g1 / (N-2);
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}
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N += 1;
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delta = x - mean;
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deltaN = delta / N;
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term1 = delta * deltaN * (N-1);
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tmp = term1 * deltaN * (N-2);
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tmp -= 3.0 * deltaN * M2;
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M3 += tmp;
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M2 += term1;
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mean += deltaN;
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if ( N < 3 ) {
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return ( isnan( M3 ) ) ? NaN : null;
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}
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// Calculate the population skewness:
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g1 = sqrt( N )*M3 / pow( M2, 1.5 );
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// Return the corrected sample skewness:
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return sqrt( N*(N-1) )*g1 / (N-2);
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}
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}
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// EXPORTS //
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module.exports = incrskewness;
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