feat(stats): add package stats/incr/nanmmda

lib/node_modules/@stdlib/stats/incr/nanmmda/README.md

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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.
+
+-->
+
+# incrnanmmda
+
+> Compute a moving [mean directional accuracy][mean-directional-accuracy] (MDA) incrementally, ignoring `NaN` values.
+
+<section class="intro">
+
+For a window of size `W`, the [mean directional accuracy][mean-directional-accuracy] is defined as
+
+<!-- <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."> -->
+
+```math
+\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}
+```
+
+<!-- <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">
+    <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.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+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].
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var incrnanmmda = require( '@stdlib/stats/incr/nanmmda' );
+```
+
+#### incrnanmmda( window )
+
+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].
+
+```javascript
+var accumulator = incrnanmmda( 3 );
+```
+
+#### accumulator( \[f, a] )
+
+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].
+
+```javascript
+var accumulator = incrnanmmda( 3 );
+
+var m = accumulator();
+// returns null
+
+m = accumulator( NaN, 4.0 );
+// returns null
+
+// Fill the window...
+m = accumulator( 2.0, 3.0 ); // [(+,+)]
+// returns 1.0
+
+m = accumulator( 1.0, 4.0 ); // [(+,+), (-,+)]
+// returns 0.5
+
+m = accumulator( 3.0, NaN ); // [(+,+), (-,+)]
+// returns 0.5
+
+m = accumulator( 3.0, 9.0 ); // [(+,+), (-,+), (+,+)]
+// returns ~0.67
+
+// Window begins sliding...
+m = accumulator( 7.0, 3.0 ); // [(-,+), (+,+), (+,-)]
+// returns ~0.33
+
+m = accumulator( NaN, NaN ); // [(-,+), (+,+), (+,-)]
+// returns -0.33
+
+m = accumulator( 5.0, 3.0 ); // [(+,+), (+,-), (-,0)]
+// returns ~0.33
+
+m = accumulator();
+// returns ~0.33
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   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.
+-   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.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var bernoulli = require( '@stdlib/random/base/bernoulli' );
+var randu = require( '@stdlib/random/base/randu' );
+var incrnanmmda = require( '@stdlib/stats/incr/nanmmda' );
+
+var accumulator;
+var v1;
+var v2;
+var i;
+
+// Initialize an accumulator:
+accumulator = incrnanmmda( 5 );
+
+// For each simulated datum, update the moving mean directional accuracy...
+for ( i = 0; i < 100; i++ ) {
+    v1 = ( bernoulli( 0.1 ) ) ? NaN : ( randu()*100.0 ) - 50.0;
+    v2 = ( bernoulli( 0.1 ) ) ? NaN : ( randu()*100.0 ) - 50.0;
+    accumulator( v1, v2 );
+}
+console.log( accumulator() );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+[mean-directional-accuracy]: https://en.wikipedia.org/wiki/Mean_Directional_Accuracy_%28MDA%29
+
+[@stdlib/math/base/special/signum]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/signum
+
+[@stdlib/math/base/special/kronecker-delta]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/kronecker-delta
+
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/stats/incr/nanmmda/benchmark/benchmark.js

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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 bench = require( '@stdlib/bench' );
+var randu = require( '@stdlib/random/base/randu' );
+var pkg = require( './../package.json' ).name;
+var incrnanmmda = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var f;
+	var i;
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		f = incrnanmmda( ( i%5 ) + 1 );
+		if ( typeof f !== 'function' ) {
+			b.fail( 'should return a function' );
+		}
+	}
+	b.toc();
+	if ( typeof f !== 'function' ) {
+		b.fail( 'should return a function' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});
+
+bench( pkg+'::accumulator', function benchmark( b ) {
+	var acc;
+	var v;
+	var i;
+
+	acc = incrnanmmda( 5 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		v = acc( randu()-0.5, randu()-0.5 );
+		if ( v !== v ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( v !== v ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});