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* @license Apache-2.0
*
* Copyright (c) 2019 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';
/**
* Returns an accumulator function which incrementally computes a weighted arithmetic mean.
*
* ## Method
*
* - The weighted arithmetic mean is defined as
*
* ```tex
* \mu = \frac{\sum_{i=0}^{n-1} w_i x_i}{\sum_{i=0}^{n-1} w_i}
* ```
*
* where \\( w_i \\) are the weights.
*
* - The weighted arithmetic mean is equivalent to the simple arithmetic mean when all weights are equal.
*
* ```tex
* \begin{align*}
* \mu &= \frac{\sum_{i=0}^{n-1} w x_i}{\sum_{i=0}^{n-1} w} \\
* &= \frac{w\sum_{i=0}^{n-1} x_i}{nw} \\
* &= \frac{1}{n} \sum_{i=0}^{n-1}
* \end{align*}
* ```
*
* - If the weights are different, then one can view weights either as sample frequencies or as a means to calculate probabilities where \\( p_i = w_i / \sum w_i \\).
*
* - To derive an incremental formula for computing a weighted arithmetic mean, let
*
* ```tex
* W_n = \sum_{i=1}^{n} w_i
* ```
*
* - Accordingly,
*
* ```tex
* \begin{align*}
* \mu_n &= \frac{1}{W_n} \sum_{i=1}^{n} w_i x_i \\
* &= \frac{1}{W_n} \biggl(w_n x_n + \sum_{i=1}^{n-1} w_i x_i \biggr) \\
* &= \frac{1}{W_n} (w_n x_n + W_{n-1} \mu_{n-1}) \\
* &= \frac{1}{W_n} (w_n x_n + (W_n - w_n) \mu_{n-1}) \\
* &= \frac{1}{W_n} (W_n \mu_{n-1} + w_n x_n - w_n\mu_{n-1}) \\
* &= \mu_{n-1} + \frac{w_n}{W_n} (x_n - \mu_{n-1})
* \end{align*}
* ```
*
* @returns {Function} accumulator function
*
* @example
* var accumulator = incrwmean();
*
* var mu = accumulator();
* // returns null
*
* mu = accumulator( 2.0, 1.0 );
* // returns 2.0
*
* mu = accumulator( 2.0, 0.5 );
* // returns 2.0
*
* mu = accumulator( 3.0, 1.5 );
* // returns 2.5
*
* mu = accumulator();
* // returns 2.5
*/
function incrwmean() {
var wsum;
var FLG;
var mu;
wsum = 0.0;
mu = 0.0;
return accumulator;
/**
* If provided arguments, the accumulator function returns an updated weighted mean. If not provided arguments, the accumulator function returns the current weighted mean.
*
* @private
* @param {number} [x] - value
* @param {number} [w] - weight
* @returns {(number|null)} weighted mean or null
*/
function accumulator( x, w ) {
if ( arguments.length === 0 ) {
if ( FLG === void 0 ) {
return null;
}
return mu;
}
FLG = true;
wsum += w;
mu += ( w/wsum ) * ( x-mu );
return mu;
}
}
// EXPORTS //
module.exports = incrwmean;
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