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