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* @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 isPositiveInteger = require( '@stdlib/assert/is-positive-integer' ).isPrimitive;
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' );
var Float64Array = require( '@stdlib/array/float64' );
var format = require( '@stdlib/string/format' );
// MAIN //
/**
* Returns an accumulator function which incrementally computes a moving corrected sample skewness.
*
* ## Method
*
* The algorithm computes the corrected sample skewness using the formula for `G_1` in [Joanes and Gill 1998][@joanes:1998]. Updates are performed using an extension of Welford's algorithm for sliding windows.
*
* ## 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
*
* @param {PositiveInteger} W - window size
* @throws {TypeError} must provide a positive integer
* @returns {Function} accumulator function
*
* @example
* var accumulator = incrmskewness( 3 );
*
* 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( 5.0 );
* // returns ~0.935
*
* skewness = accumulator();
* // returns ~0.935
*/
function incrmskewness( W ) {
var deltaN;
var term1;
var delta;
var mean;
var buf;
var tmp;
var g1;
var M2;
var M3;
var i;
var N;
if ( !isPositiveInteger( W ) ) {
throw new TypeError( format( 'invalid argument. Must provide a positive integer. Value: `%s`.', W ) );
}
buf = new Float64Array( W );
mean = 0.0;
M2 = 0.0;
M3 = 0.0;
i = -1;
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 ) {
var meanOld;
var M2Old;
var v;
var k;
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 );
}
// Update the index for managing the circular buffer:
i = ( i + 1 ) % W;
// Case: incoming value is NaN, so the accumulated statistics are automatically NaN...
if ( isnan( x ) ) {
M2 = NaN;
M3 = NaN;
mean = NaN;
N = W; // explicitly set to avoid `N < W` branch
}
// Case: initial window...
else if ( N < W ) {
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;
}
// Case: outgoing value is NaN or current stats are NaN, and, thus, we need to recompute the accumulated values...
else if ( isnan( buf[ i ] ) || isnan( M2 ) || isnan( M3 ) ) {
N = 0;
M2 = 0.0;
M3 = 0.0;
mean = 0.0;
// Reconstruct statistics from the buffer (excluding the outgoing value at `i`, adding `x`):
for ( k = 0; k < W; k++ ) {
v = ( k === i ) ? x : buf[ k ];
if ( isnan( v ) ) {
N = W;
M2 = NaN;
M3 = NaN;
mean = NaN;
break;
}
N += 1;
delta = v - 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;
}
}
// Case: neither the current stats nor the incoming/outgoing values are NaN, so we update the accumulated values (remove old, add new)...
else {
// Remove the outgoing value (buf[i]):
v = buf[ i ];
// To remove, we reverse the Welford update. We calculate the mean *before* v was added (which corresponds to N-1). N here is W.
meanOld = ( ( N * mean ) - v ) / ( N - 1 );
delta = v - meanOld;
deltaN = delta / N; // This is ( mean - meanOld )
term1 = delta * deltaN * ( N - 1 );
// Revert M2 first (order matters relative to add operation, but we need M2_old for M3):
M2Old = M2 - term1;
tmp = term1 * deltaN * ( N - 2 );
tmp -= 3.0 * deltaN * M2Old;
M3 -= tmp;
M2 = M2Old;
mean = meanOld;
// Now Add the new value (x)
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;
}
buf[ i ] = x;
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 = incrmskewness;
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