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feat: add stats/incr/nanmme
PR-URL: #9460 Closes: #5587 Co-authored-by: Philipp Burckhardt <pburckhardt@outlook.com> Co-authored-by: stdlib-bot <noreply@stdlib.io> Reviewed-by: Philipp Burckhardt <pburckhardt@outlook.com>
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‎lib/node_modules/@stdlib/stats/incr/nanmme/README.md‎

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<!--
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@license Apache-2.0
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Copyright (c) 2026 The Stdlib Authors.
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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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http://www.apache.org/licenses/LICENSE-2.0
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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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# incrnanmme
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> Compute a moving [mean error][mean-absolute-error] (ME) incrementally, ignoring `NaN` values.
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<section class="intro">
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For a window of size `W`, the [mean error][mean-absolute-error] is defined as
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<!-- <equation class="equation" label="eq:mean_error" align="center" raw="\mathop{\mathrm{ME}} = \frac{1}{W} \sum_{i=0}^{W-1} (y_i - x_i)" alt="Equation for the mean error."> -->
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```math
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\mathop{\mathrm{ME}} = \frac{1}{W} \sum_{i=0}^{W-1} (y_i - x_i)
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```
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<!-- <div class="equation" align="center" data-raw-text="\operatorname{ME} = \frac{1}{W} \sum_{i=0}^{W-1} (y_i - x_i)" data-equation="eq:mean_error">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@634ac3689760e2f57fd51085f387d8dc5bb3b927/lib/node_modules/@stdlib/stats/incr/nanmme/docs/img/equation_mean_error.svg" alt="Equation for the mean error.">
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<br>
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</div> -->
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<!-- </equation> -->
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var incrnanmme = require( '@stdlib/stats/incr/nanmme' );
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```
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#### incrnanmme( window )
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Returns an accumulator `function` which incrementally computes a moving [mean error][mean-absolute-error], ignoring any `(x, y)` pairs containing `NaN`. The `window` parameter defines the number of values over which to compute the moving [mean error][mean-absolute-error].
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```javascript
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var accumulator = incrnanmme( 3 );
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```
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#### accumulator( \[x, y] )
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If provided input values `x` and `y`, the accumulator function returns an updated [mean error][mean-absolute-error]. If not provided input values `x` and `y`, the accumulator function returns the current [mean error][mean-absolute-error].
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```javascript
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var accumulator = incrnanmme( 3 );
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var m = accumulator();
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// returns null
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// Fill the window...
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m = accumulator( 2.0, 3.0 ); // [(2.0, 3.0)]
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// returns 1.0
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m = accumulator( -5.0, 2.0 ); // [(2.0, 3.0), (-5.0, 2.0)]
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// returns 4.0
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m = accumulator( 3.0, NaN ); // NaN pair ignored: [(2.0, 3.0), (-5.0, 2.0)]
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// returns 4.0
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// Window begins sliding...
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m = accumulator( -7.0, 3.0 ); // [(2.0, 3.0), (-5.0, 2.0), (-7.0, 3.0)]
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// returns 6.0
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m = accumulator( -5.0, -3.0 ); // [(-5.0, 2.0), (-7.0, 3.0), (-5.0, -3.0)]
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// returns ~6.33
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m = accumulator();
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// returns ~6.33
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- Input values are **not** type checked. Any `(x, y)` pair containing `NaN` is ignored and does **not** update the window.
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- As `W` (x,y) pairs are needed to fill the window buffer, the first `W-1` returned values are calculated from smaller sample sizes. Until the window is full, each returned value is calculated from all provided values.
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- Be careful when interpreting the [mean error][mean-absolute-error] as errors can cancel. This stated, that errors can cancel makes the [mean error][mean-absolute-error] suitable for measuring the bias in forecasts.
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- **Warning**: the [mean error][mean-absolute-error] is scale-dependent and, thus, the measure should **not** be used to make comparisons between datasets having different scales.
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var randu = require( '@stdlib/random/base/randu' );
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var incrnanmme = require( '@stdlib/stats/incr/nanmme' );
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var accumulator;
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var v1;
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var v2;
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var i;
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// Initialize an accumulator:
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accumulator = incrnanmme( 5 );
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// For each simulated datum, update the moving mean error...
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for ( i = 0; i < 100; i++ ) {
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v1 = ( randu()*100.0 ) - 50.0;
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v2 = ( randu()*100.0 ) - 50.0;
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accumulator( v1, v2 );
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}
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console.log( accumulator() );
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```
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</section>
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<!-- /.examples -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[mean-absolute-error]: https://en.wikipedia.org/wiki/Mean_absolute_error
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<!-- <related-links> -->
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<!-- </related-links> -->
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</section>
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<!-- /.links -->
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‎lib/node_modules/@stdlib/stats/incr/nanmme/benchmark/benchmark.js‎

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2026 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 bench = require( '@stdlib/bench' );
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var randu = require( '@stdlib/random/base/randu' );
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var format = require( '@stdlib/string/format' );
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var pkg = require( './../package.json' ).name;
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var incrnanmme = require( './../lib' );
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// MAIN //
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bench( pkg, function benchmark( b ) {
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var f;
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var i;
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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f = incrnanmme( ( i % 5 ) + 1 );
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if ( typeof f !== 'function' ) {
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b.fail( 'should return a function' );
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}
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}
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b.toc();
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if ( typeof f !== 'function' ) {
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b.fail( 'should return a function' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});
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bench( format( '%s::accumulator', pkg ), function benchmark( b ) {
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var acc;
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var v;
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var i;
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acc = incrnanmme( 5 );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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v = acc( randu() - 0.5, randu() - 0.5 );
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if ( v !== v ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( v !== v ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});
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bench( format( '%s::accumulator-nan', pkg ), function benchmark( b ) {
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var acc;
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var v;
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var i;
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acc = incrnanmme( 5 );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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if ( i % 10 === 0 ) {
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v = acc( NaN, randu() - 0.5 );
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} else {
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v = acc( randu() - 0.5, randu() - 0.5 );
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}
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if ( v !== v ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( v !== v ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});

‎lib/node_modules/@stdlib/stats/incr/nanmme/docs/img/equation_mean_error.svg‎

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‎lib/node_modules/@stdlib/stats/incr/nanmme/docs/repl.txt‎

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{{alias}}( W )
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Returns an accumulator function which incrementally computes a moving
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mean error (ME), ignoring `NaN` values.
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The `W` parameter defines the number of values over which to compute the
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moving mean error.
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If provided input values, the accumulator function returns an updated
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moving mean error. If not provided input values, the accumulator function
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returns the current moving mean error.
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As `W` (x,y) pairs are needed to fill the window buffer, the first `W-1`
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returned values are calculated from smaller sample sizes. Until the window
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is full, each returned value is calculated from all provided values which
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are not `NaN`.
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Parameters
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----------
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W: integer
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Window size.
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Returns
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-------
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acc: Function
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Accumulator function.
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Examples
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--------
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> var accumulator = {{alias}}( 3 );
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> var m = accumulator()
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null
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> m = accumulator( 2.0, 3.0 )
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1.0
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> m = accumulator( -5.0, NaN )
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1.0
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> m = accumulator( 3.0, 2.0 )
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0.0
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> m = accumulator( 5.0, -2.0 )
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~-2.33
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> m = accumulator()
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~-2.33
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See Also
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--------
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‎lib/node_modules/@stdlib/stats/incr/nanmme/docs/types/index.d.ts‎

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/*
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* @license Apache-2.0
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*
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* Copyright (c) 2026 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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// TypeScript Version: 4.1
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/// <reference types="@stdlib/types"/>
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/**
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* If provided input values, the accumulator function returns an updated mean error. If not provided input values, the accumulator function returns the current mean error.
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*
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* ## Notes
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*
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* - If either `x` or `y` is `NaN`, the pair is ignored and the accumulator returns the previously accumulated value.
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*
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* @param x - input value
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* @param y - input value
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* @returns mean error or null
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*/
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type accumulator = ( x?: number, y?: number ) => number | null;
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/**
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* Returns an accumulator function which incrementally computes a moving mean error (ME), ignoring `NaN` values.
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*
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* ## Notes
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*
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* - The `W` parameter defines the number of values over which to compute the moving mean error.
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* - As `W` (x,y) pairs are needed to fill the window buffer, the first `W-1` returned values are calculated from smaller sample sizes. Until the window is full, each returned value is calculated from all provided values.
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*
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* @param W - window size
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* @throws must provide a positive integer
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* @returns accumulator function
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*
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* @example
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* var accumulator = incrnanmme( 3 );
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*
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* var m = accumulator();
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* // returns null
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*
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* m = accumulator( 2.0, 3.0 );
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* // returns 1.0
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*
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* m = accumulator( -5.0, 2.0 );
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* // returns 4.0
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*
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* m = accumulator( 3.0, NaN );
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* // returns 4.0
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*
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* m = accumulator( -7.0, 3.0 );
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* // returns 6.0
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*
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* m = accumulator( -5.0, -3.0 );
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* // returns ~6.33
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*
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* m = accumulator();
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* // returns ~6.33
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*/
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declare function incrnanmme( W: number ): accumulator;
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// EXPORTS //
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export = incrnanmme;

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