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feat(stats): add package
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‎lib/node_modules/@stdlib/stats/incr/nanmmda/README.md

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<!--
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@license Apache-2.0
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Copyright (c) 2025 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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# incrnanmmda
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> Compute a moving [mean directional accuracy][mean-directional-accuracy] (MDA) incrementally, ignoring `NaN` values.
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<section class="intro">
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For a window of size `W`, the [mean directional accuracy][mean-directional-accuracy] is defined as
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<!-- <equation class="equation" label="eq:mean_directional_accuracy" align="center" raw="\operatorname{MDA} = \begin{cases} 1 & \textrm{if}\ W = 1 \\ \frac{1}{W} \sum_{i=1}^{W} \delta_{\operatorname{sgn}(\Delta f_{i,i-1}),\ \operatorname{sgn}(\Delta a_{i,i-1})} & \textrm{if}\ W > 1 \end{cases}" alt="Equation for the mean directional accuracy."> -->
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```math
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\mathop{\mathrm{MDA}} = \begin{cases} 1 & \textrm{if}\ W = 1 \\ \frac{1}{W} \sum_{i=1}^{W} \delta_{\mathop{\mathrm{sgn}}(\Delta f_{i,i-1}),\ \mathop{\mathrm{sgn}}(\Delta a_{i,i-1})} & \textrm{if}\ W > 1 \end{cases}
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```
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<!-- <div class="equation" align="center" data-raw-text="\operatorname{MDA} = \begin{cases} 1 & \textrm{if}\ W = 1 \\\frac{1}{W} \sum_{i=1}^{W} \delta_{\operatorname{sgn}(\Delta f_{i,i-1}),\ \operatorname{sgn}(\Delta a_{i,i-1})} & \textrm{if}\ W > 1 \end{cases}" data-equation="eq:mean_directional_accuracy">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@99730afbace8256ce53cfbc0714c7f3cac92466a/lib/node_modules/@stdlib/stats/incr/mmda/docs/img/equation_mean_directional_accuracy.svg" alt="Equation for the mean directional accuracy.">
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<br>
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</div> -->
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<!-- </equation> -->
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where `f_i` is the forecast value, `a_i` is the actual value, `sgn(x)` is the [signum][@stdlib/math/base/special/signum] function, and `δ` is the [Kronecker delta][@stdlib/math/base/special/kronecker-delta].
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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 incrnanmmda = require( '@stdlib/stats/incr/nanmmda' );
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```
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#### incrnanmmda( window )
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Returns an accumulator `function` which incrementally computes a moving [mean directional accuracy][mean-directional-accuracy], ignoring `NaN` values. The `window` parameter defines the number of values over which to compute the moving [mean directional accuracy][mean-directional-accuracy].
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```javascript
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var accumulator = incrnanmmda( 3 );
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```
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#### accumulator( \[f, a] )
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If provided input values `f` and `a`, the accumulator function returns an updated [mean directional accuracy][mean-directional-accuracy]. If not provided input values `f` and `a`, the accumulator function returns the current [mean directional accuracy][mean-directional-accuracy].
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```javascript
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var accumulator = incrnanmmda( 3 );
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var m = accumulator();
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// returns null
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m = accumulator( NaN, 4.0 );
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// returns null
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// Fill the window...
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m = accumulator( 2.0, 3.0 ); // [(+,+)]
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// returns 1.0
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m = accumulator( 1.0, 4.0 ); // [(+,+), (-,+)]
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// returns 0.5
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m = accumulator( 3.0, NaN ); // [(+,+), (-,+)]
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// returns 0.5
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m = accumulator( 3.0, 9.0 ); // [(+,+), (-,+), (+,+)]
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// returns ~0.67
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// Window begins sliding...
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m = accumulator( 7.0, 3.0 ); // [(-,+), (+,+), (+,-)]
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// returns ~0.33
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m = accumulator( NaN, NaN ); // [(-,+), (+,+), (+,-)]
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// returns -0.33
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m = accumulator( 5.0, 3.0 ); // [(+,+), (+,-), (-,0)]
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// returns ~0.33
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m = accumulator();
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// returns ~0.33
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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. If provided `NaN` or a value which, when used in computations, results in `NaN`, the accumulated value is **not** changed and the current input values get **ignored**. If non-numeric inputs are possible, you are advised to type check and handle accordingly **before** passing the value to the accumulator function.
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- As `W` (f,a) 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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</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 bernoulli = require( '@stdlib/random/base/bernoulli' );
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var randu = require( '@stdlib/random/base/randu' );
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var incrnanmmda = require( '@stdlib/stats/incr/nanmmda' );
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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 = incrnanmmda( 5 );
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// For each simulated datum, update the moving mean directional accuracy...
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for ( i = 0; i < 100; i++ ) {
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v1 = ( bernoulli( 0.1 ) ) ? NaN : ( randu()*100.0 ) - 50.0;
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v2 = ( bernoulli( 0.1 ) ) ? NaN : ( 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 related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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* * *
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## See Also
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- <span class="package-name">[`@stdlib/stats/incr/mda`][@stdlib/stats/incr/mda]</span><span class="delimiter">: </span><span class="description">compute the mean directional accuracy (MDA) incrementally.</span>
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- <span class="package-name">[`@stdlib/stats/incr/mmape`][@stdlib/stats/incr/mmape]</span><span class="delimiter">: </span><span class="description">compute a moving mean absolute percentage error (MAPE) incrementally.</span>
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</section>
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<!-- /.related -->
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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-directional-accuracy]: https://en.wikipedia.org/wiki/Mean_Directional_Accuracy_%28MDA%29
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[@stdlib/math/base/special/signum]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/signum
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[@stdlib/math/base/special/kronecker-delta]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/kronecker-delta
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<!-- <related-links> -->
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[@stdlib/stats/incr/mda]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/mda
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[@stdlib/stats/incr/mmape]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/mmape
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<!-- </related-links> -->
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/stats/incr/nanmmda/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) 2025 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 pkg = require( './../package.json' ).name;
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var incrnanmmda = 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 = incrnanmmda( (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( pkg+'::accumulator', 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 = incrnanmmda( 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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