diff --git a/lib/node_modules/@stdlib/stats/incr/nanmcovariance/README.md b/lib/node_modules/@stdlib/stats/incr/nanmcovariance/README.md
new file mode 100644
index 000000000000..35d3dc1200b7
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmcovariance/README.md
@@ -0,0 +1,183 @@
+
+
+# incrnanmcovariance
+
+> Compute a moving [unbiased sample covariance][covariance] incrementally, ignoring `NaN` values.
+
+
+
+For unknown population means, the [unbiased sample covariance][covariance] for a window `n` of size `W` is defined as
+
+
+
+```math
+\mathop{\mathrm{cov_n}} = \frac{1}{n-1} \sum_{i=j}^{j+W-1} (x_i - \bar{x}_n)(y_i - \bar{y}_n)
+```
+
+
+
+
+
+where `j` specifies the index of the value at which the window begins. For example, for a trailing (i.e., non-centered) window using zero-based indexing and `j` greater than or equal to `W`, `j` is the `n-W`th value with `n` being the number of values thus analyzed.
+
+For known population means, the [unbiased sample covariance][covariance] for a window `n` of size `W` is defined as
+
+
+
+```math
+\mathop{\mathrm{cov_n}} = \frac{1}{n} \sum_{i=j}^{j+W-1} (x_i - \mu_x)(y_i - \mu_y)
+```
+
+
+
+
+
+
+
+
+
+
+
+## Usage
+
+```javascript
+var incrnanmcovariance = require( '@stdlib/stats/incr/nanmcovariance' );
+```
+
+#### incrnanmcovariance( window\[, mx, my] )
+
+Returns an accumulator `function` which incrementally computes a moving [unbiased sample covariance][covariance], ignoring `NaN` values. The `window` parameter defines the number of values over which to compute the moving [unbiased sample covariance][covariance].
+
+```javascript
+var accumulator = incrnanmcovariance( 3 );
+```
+
+If means are already known, provide `mx` and `my` arguments.
+
+```javascript
+var accumulator = incrnanmcovariance( 3, 5.0, -3.14 );
+```
+
+#### accumulator( \[x, y] )
+
+If provided input values `x` and `y`, the accumulator function returns an updated [unbiased sample covariance][covariance]. If not provided input values `x` and `y`, the accumulator function returns the current [unbiased sample covariance][covariance].
+
+```javascript
+var accumulator = incrnanmcovariance( 3 );
+
+var v = accumulator();
+// returns null
+
+// Fill the window...
+v = accumulator( 2.0, 1.0 ); // [(2.0, 1.0)]
+// returns 0.0
+
+v = accumulator( NaN, 1.0 ); // [(2.0, 1.0)]
+// returns 0.0
+
+v = accumulator( -5.0, 3.14 ); // [(2.0, 1.0), (-5.0, 3.14)]
+// returns ~-7.49
+
+v = accumulator( 3.0, -1.0 ); // [(2.0, 1.0), (-5.0, 3.14), (3.0, -1.0)]
+// returns -8.35
+
+// Window begins sliding...
+v = accumulator( 5.0, -9.5 ); // [(-5.0, 3.14), (3.0, -1.0), (5.0, -9.5)]
+// returns -29.42
+
+v = accumulator( -5.0, 1.5 ); // [(3.0, -1.0), (5.0, -9.5), (-5.0, 1.5)]
+// returns -24.5
+
+v = accumulator();
+// returns -24.5
+```
+
+
+
+
+
+
+
+## Notes
+
+- Input values are **not** type checked. 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` (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.
+
+
+
+
+
+
+
+## Examples
+
+
+
+```javascript
+var uniform = require( '@stdlib/random/base/uniform' );
+var bernoulli = require( '@stdlib/random/base/bernoulli' );
+var incrnanmcovariance = require( '@stdlib/stats/incr/nanmcovariance' );
+
+var accumulator;
+var x;
+var y;
+var i;
+
+// Initialize an accumulator:
+accumulator = incrnanmcovariance( 5 );
+
+// For each simulated datum, update the moving unbiased sample covariance...
+for ( i = 0; i < 100; i++ ) {
+ x = ( bernoulli( 0.8 ) < 1 ) ? NaN : uniform( 0.0, 100.0 );
+ y = ( bernoulli( 0.8 ) < 1 ) ? NaN : uniform( 0.0, 100.0 );
+ accumulator( x, y );
+}
+console.log( accumulator() );
+```
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+[covariance]: https://en.wikipedia.org/wiki/Covariance
+
+
+
+
+
diff --git a/lib/node_modules/@stdlib/stats/incr/nanmcovariance/benchmark/benchmark.js b/lib/node_modules/@stdlib/stats/incr/nanmcovariance/benchmark/benchmark.js
new file mode 100644
index 000000000000..859076f57758
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmcovariance/benchmark/benchmark.js
@@ -0,0 +1,92 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 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 format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var incrnanmcovariance = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+ var f;
+ var i;
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ f = incrnanmcovariance( (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( format( '%s::accumulator', pkg ), function benchmark( b ) {
+ var acc;
+ var v;
+ var i;
+
+ acc = incrnanmcovariance( 5 );
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ v = acc( randu(), randu() );
+ 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();
+});
+
+bench( format( '%s::accumulator,known_means', pkg ), function benchmark( b ) {
+ var acc;
+ var v;
+ var i;
+
+ acc = incrnanmcovariance( 5, 3.0, -1.0 );
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ v = acc( randu(), randu() );
+ 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();
+});
diff --git a/lib/node_modules/@stdlib/stats/incr/nanmcovariance/docs/img/equation_unbiased_sample_covariance_known_means.svg b/lib/node_modules/@stdlib/stats/incr/nanmcovariance/docs/img/equation_unbiased_sample_covariance_known_means.svg
new file mode 100644
index 000000000000..b36fb46a6a8f
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmcovariance/docs/img/equation_unbiased_sample_covariance_known_means.svg
@@ -0,0 +1,76 @@
+
\ No newline at end of file
diff --git a/lib/node_modules/@stdlib/stats/incr/nanmcovariance/docs/img/equation_unbiased_sample_covariance_unknown_means.svg b/lib/node_modules/@stdlib/stats/incr/nanmcovariance/docs/img/equation_unbiased_sample_covariance_unknown_means.svg
new file mode 100644
index 000000000000..1d8750e5494a
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmcovariance/docs/img/equation_unbiased_sample_covariance_unknown_means.svg
@@ -0,0 +1,82 @@
+
\ No newline at end of file
diff --git a/lib/node_modules/@stdlib/stats/incr/nanmcovariance/docs/repl.txt b/lib/node_modules/@stdlib/stats/incr/nanmcovariance/docs/repl.txt
new file mode 100644
index 000000000000..32faf2d5cede
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmcovariance/docs/repl.txt
@@ -0,0 +1,53 @@
+
+{{alias}}( W[, mx, my] )
+ Returns an accumulator function which incrementally computes a moving
+ unbiased sample covariance, ignoring `NaN` values.
+
+ The `W` parameter defines the number of values over which to compute the
+ moving unbiased sample covariance.
+
+ If provided values, the accumulator function returns an updated moving
+ unbiased sample covariance. If not provided values, the accumulator function
+ returns the current moving unbiased sample covariance.
+
+ 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.
+
+ Parameters
+ ----------
+ W: integer
+ Window size.
+
+ mx: number (optional)
+ Known mean.
+
+ my: number (optional)
+ Known mean.
+
+ Returns
+ -------
+ acc: Function
+ Accumulator function.
+
+ Examples
+ --------
+ > var accumulator = {{alias}}( 3 );
+ > var v = accumulator()
+ null
+ > v = accumulator( 2.0, 1.0 )
+ 0.0
+ > v = accumulator( NaN, 1.0 )
+ 0.0
+ > v = accumulator( -5.0, 3.14 )
+ ~-7.49
+ > v = accumulator( 3.0, -1.0 )
+ -8.35
+ > v = accumulator( 5.0, -9.5 )
+ -29.42
+ > v = accumulator()
+ -29.42
+
+ See Also
+ --------
+
diff --git a/lib/node_modules/@stdlib/stats/incr/nanmcovariance/docs/types/index.d.ts b/lib/node_modules/@stdlib/stats/incr/nanmcovariance/docs/types/index.d.ts
new file mode 100644
index 000000000000..f06386deda64
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmcovariance/docs/types/index.d.ts
@@ -0,0 +1,92 @@
+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2026 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.
+*/
+
+// TypeScript Version: 4.1
+
+///
+
+/**
+* If provided arguments, returns an updated moving unbiased sample covariance; otherwise, returns the current moving unbiased sample covariance.
+*
+* @param x - value
+* @param y - value
+* @returns moving unbiased sample covariance
+*/
+type accumulator = ( x?: number, y?: number ) => number | null;
+
+/**
+* Returns an accumulator function which incrementally computes a moving unbiased sample covariance, ignoring `NaN` values.
+*
+* ## Notes
+*
+* - The `W` parameter defines the number of values over which to compute the moving unbiased sample covariance.
+* - 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.
+*
+* @param W - window size
+* @param meanx - mean value
+* @param meany - mean value
+* @throws first argument must be a positive integer
+* @returns accumulator function
+*
+* @example
+* var accumulator = incrnanmcovariance( 3, -2.0, 10.0 );
+*/
+declare function incrnanmcovariance( W: number, meanx: number, meany: number ): accumulator;
+
+/**
+* Returns an accumulator function which incrementally computes a moving unbiased sample covariance.
+*
+* ## Notes
+*
+* - The `W` parameter defines the number of values over which to compute the moving unbiased sample covariance.
+* - 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.
+*
+* @param W - window size
+* @throws first argument must be a positive integer
+* @returns accumulator function
+*
+* @example
+* var accumulator = incrnanmcovariance( 3 );
+*
+* var v = accumulator();
+* // returns null
+*
+* v = accumulator( 2.0, 1.0 );
+* // returns 0.0
+*
+* v = accumulator( NaN, 1.0 );
+* // returns 0.0
+*
+* v = accumulator( -5.0, 3.14 );
+* // returns ~-7.49
+*
+* v = accumulator( 3.0, -1.0 );
+* // returns -8.35
+*
+* v = accumulator( 5.0, -9.5 );
+* // returns -29.42
+*
+* v = accumulator();
+* // returns -29.42
+*/
+declare function incrnanmcovariance( W: number ): accumulator;
+
+
+// EXPORTS //
+
+export = incrnanmcovariance;
diff --git a/lib/node_modules/@stdlib/stats/incr/nanmcovariance/docs/types/test.ts b/lib/node_modules/@stdlib/stats/incr/nanmcovariance/docs/types/test.ts
new file mode 100644
index 000000000000..996ee9cb3312
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmcovariance/docs/types/test.ts
@@ -0,0 +1,123 @@
+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2026 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.
+*/
+
+import incrcovariance = require( './index' );
+
+
+// TESTS //
+
+// The function returns an accumulator function...
+{
+ incrcovariance( 3 ); // $ExpectType accumulator
+ incrcovariance( 3, 2, 4 ); // $ExpectType accumulator
+}
+
+// The compiler throws an error if the function is provided non-numeric arguments...
+{
+ incrcovariance( 2, '5' ); // $ExpectError
+ incrcovariance( 2, true ); // $ExpectError
+ incrcovariance( 2, false ); // $ExpectError
+ incrcovariance( 2, null ); // $ExpectError
+ incrcovariance( 2, undefined ); // $ExpectError
+ incrcovariance( 2, [] ); // $ExpectError
+ incrcovariance( 2, {} ); // $ExpectError
+ incrcovariance( 2, ( x: number ): number => x ); // $ExpectError
+
+ incrcovariance( '5', 4 ); // $ExpectError
+ incrcovariance( true, 4 ); // $ExpectError
+ incrcovariance( false, 4 ); // $ExpectError
+ incrcovariance( null, 4 ); // $ExpectError
+ incrcovariance( undefined, 4 ); // $ExpectError
+ incrcovariance( [], 4 ); // $ExpectError
+ incrcovariance( {}, 4 ); // $ExpectError
+ incrcovariance( ( x: number ): number => x, 4 ); // $ExpectError
+
+ incrcovariance( '5', 2.5, 3.5 ); // $ExpectError
+ incrcovariance( true, 2.5, 3.5 ); // $ExpectError
+ incrcovariance( false, 2.5, 3.5 ); // $ExpectError
+ incrcovariance( null, 2.5, 3.5 ); // $ExpectError
+ incrcovariance( undefined, 2.5, 3.5 ); // $ExpectError
+ incrcovariance( [], 2.5, 3.5 ); // $ExpectError
+ incrcovariance( {}, 2.5, 3.5 ); // $ExpectError
+ incrcovariance( ( x: number ): number => x, 2.5, 3.5 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided an invalid number of arguments...
+{
+ incrcovariance(); // $ExpectError
+ incrcovariance( 1, 2 ); // $ExpectError
+ incrcovariance( 2, 2, 3, 4 ); // $ExpectError
+}
+
+// The function returns an accumulator function which returns an accumulated result...
+{
+ const acc = incrcovariance( 3 );
+
+ acc(); // $ExpectType number | null
+ acc( 3.14, 2.0 ); // $ExpectType number | null
+}
+
+// The function returns an accumulator function which returns an accumulated result (known means)...
+{
+ const acc = incrcovariance( 3, 2, -3 );
+
+ acc(); // $ExpectType number | null
+ acc( 3.14, 2.0 ); // $ExpectType number | null
+}
+
+// The compiler throws an error if the returned accumulator function is provided invalid arguments...
+{
+ const acc = incrcovariance( 3 );
+
+ acc( '5', 1.0 ); // $ExpectError
+ acc( true, 1.0 ); // $ExpectError
+ acc( false, 1.0 ); // $ExpectError
+ acc( null, 1.0 ); // $ExpectError
+ acc( [], 1.0 ); // $ExpectError
+ acc( {}, 1.0 ); // $ExpectError
+ acc( ( x: number ): number => x, 1.0 ); // $ExpectError
+
+ acc( 3.14, '5' ); // $ExpectError
+ acc( 3.14, true ); // $ExpectError
+ acc( 3.14, false ); // $ExpectError
+ acc( 3.14, null ); // $ExpectError
+ acc( 3.14, [] ); // $ExpectError
+ acc( 3.14, {} ); // $ExpectError
+ acc( 3.14, ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the returned accumulator function is provided invalid arguments (known means)...
+{
+ const acc = incrcovariance( 3, 2, -3 );
+
+ acc( '5', 1.0 ); // $ExpectError
+ acc( true, 1.0 ); // $ExpectError
+ acc( false, 1.0 ); // $ExpectError
+ acc( null, 1.0 ); // $ExpectError
+ acc( [], 1.0 ); // $ExpectError
+ acc( {}, 1.0 ); // $ExpectError
+ acc( ( x: number ): number => x, 1.0 ); // $ExpectError
+
+ acc( 3.14, '5' ); // $ExpectError
+ acc( 3.14, true ); // $ExpectError
+ acc( 3.14, false ); // $ExpectError
+ acc( 3.14, null ); // $ExpectError
+ acc( 3.14, [] ); // $ExpectError
+ acc( 3.14, {} ); // $ExpectError
+ acc( 3.14, ( x: number ): number => x ); // $ExpectError
+}
diff --git a/lib/node_modules/@stdlib/stats/incr/nanmcovariance/examples/index.js b/lib/node_modules/@stdlib/stats/incr/nanmcovariance/examples/index.js
new file mode 100644
index 000000000000..c788f22f2009
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmcovariance/examples/index.js
@@ -0,0 +1,41 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 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';
+
+var uniform = require( '@stdlib/random/base/uniform' );
+var bernoulli = require( '@stdlib/random/base/bernoulli' );
+var incrnanmcovariance = require( './../lib' );
+
+var accumulator;
+var cov;
+var x;
+var y;
+var i;
+
+// Initialize an accumulator:
+accumulator = incrnanmcovariance( 5 );
+
+// For each simulated datum, update the moving unbiased sample covariance...
+console.log( '\nx\ty\tSample Covariance\n' );
+for ( i = 0; i < 100; i++ ) {
+ x = ( bernoulli( 0.8 ) < 1 ) ? NaN : uniform( 0.0, 100.0 );
+ y = ( bernoulli( 0.8 ) < 1 ) ? NaN : uniform( 0.0, 100.0 );
+ cov = accumulator( x, y );
+ console.log( '%d\t%d\t%d', x.toFixed( 4 ), y.toFixed( 4 ), ( cov === null ) ? NaN : cov.toFixed( 4 ) );
+}
diff --git a/lib/node_modules/@stdlib/stats/incr/nanmcovariance/lib/index.js b/lib/node_modules/@stdlib/stats/incr/nanmcovariance/lib/index.js
new file mode 100644
index 000000000000..6e3b85e3f337
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmcovariance/lib/index.js
@@ -0,0 +1,60 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 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';
+
+/**
+* Compute a moving unbiased sample covariance incrementally, ignoring `NaN` values.
+*
+* @module @stdlib/stats/incr/nanmcovariance
+*
+* @example
+* var incrnanmcovariance = require( '@stdlib/stats/incr/nanmcovariance' );
+*
+* var accumulator = incrnanmcovariance( 3 );
+*
+* var v = accumulator();
+* // returns null
+*
+* v = accumulator( 2.0, 1.0 );
+* // returns 0.0
+*
+* v = accumulator( NaN, 1.0 );
+* // returns 0.0
+*
+* v = accumulator( -5.0, 3.14 );
+* // returns ~-7.49
+*
+* v = accumulator( 3.0, -1.0 );
+* // returns -8.35
+*
+* v = accumulator( 5.0, -9.5 );
+* // returns -29.42
+*
+* v = accumulator();
+* // returns -29.42
+*/
+
+// MODULES //
+
+var main = require( './main.js' );
+
+
+// EXPORTS //
+
+module.exports = main;
diff --git a/lib/node_modules/@stdlib/stats/incr/nanmcovariance/lib/main.js b/lib/node_modules/@stdlib/stats/incr/nanmcovariance/lib/main.js
new file mode 100644
index 000000000000..af576a93e7a7
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmcovariance/lib/main.js
@@ -0,0 +1,95 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 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 isnan = require( '@stdlib/math/base/assert/is-nan' );
+var incrmcovariance = require( '@stdlib/stats/incr/mcovariance' );
+
+
+// MAIN //
+
+/**
+* Returns an accumulator function which incrementally computes a moving unbiased sample covariance, ignoring `NaN` values.
+*
+* @param {PositiveInteger} W - window size
+* @param {number} [meanx] - mean value
+* @param {number} [meany] - mean value
+* @throws {TypeError} first argument must be a positive integer
+* @throws {TypeError} second argument must be a number
+* @throws {TypeError} third argument must be a number
+* @returns {Function} accumulator function
+*
+* @example
+* var accumulator = incrnanmcovariance( 3 );
+*
+* var v = accumulator();
+* // returns null
+*
+* v = accumulator( 2.0, 1.0 );
+* // returns 0.0
+*
+* v = accumulator( NaN, 1.0 );
+* // returns 0.0
+*
+* v = accumulator( -5.0, 3.14 );
+* // returns ~-7.49
+*
+* v = accumulator( 3.0, -1.0 );
+* // returns -8.35
+*
+* v = accumulator( 5.0, -9.5 );
+* // returns -29.42
+*
+* v = accumulator();
+* // returns -29.42
+*
+* @example
+* var accumulator = incrnanmcovariance( 3, -2.0, 10.0 );
+*/
+function incrnanmcovariance( W, meanx, meany ) {
+ var acc;
+ if ( arguments.length > 1 ) {
+ acc = incrmcovariance( W, meanx, meany );
+ } else {
+ acc = incrmcovariance( W );
+ }
+ return accumulator;
+
+ /**
+ * If provided a value, the accumulator function returns an updated unbiased sample covariance. If not provided a value, the accumulator function returns the current unbiased sample covariance.
+ *
+ * @private
+ * @param {number} [x] - input value
+ * @param {number} [y] - input value
+ * @returns {(number|null)} unbiased sample covariance or null
+ */
+ function accumulator( x, y ) {
+ if ( arguments.length === 0 || isnan( x ) || isnan( y ) ) {
+ return acc();
+ }
+ return acc( x, y );
+ }
+}
+
+
+// EXPORTS //
+
+module.exports = incrnanmcovariance;
diff --git a/lib/node_modules/@stdlib/stats/incr/nanmcovariance/package.json b/lib/node_modules/@stdlib/stats/incr/nanmcovariance/package.json
new file mode 100644
index 000000000000..ada235e73b13
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmcovariance/package.json
@@ -0,0 +1,77 @@
+{
+ "name": "@stdlib/stats/incr/nanmcovariance",
+ "version": "0.0.0",
+ "description": "Compute a moving unbiased sample covariance incrementally, ignoring NaN values.",
+ "license": "Apache-2.0",
+ "author": {
+ "name": "The Stdlib Authors",
+ "url": "https://github.com/stdlib-js/stdlib/graphs/contributors"
+ },
+ "contributors": [
+ {
+ "name": "The Stdlib Authors",
+ "url": "https://github.com/stdlib-js/stdlib/graphs/contributors"
+ }
+ ],
+ "main": "./lib",
+ "directories": {
+ "benchmark": "./benchmark",
+ "doc": "./docs",
+ "example": "./examples",
+ "lib": "./lib",
+ "test": "./test"
+ },
+ "types": "./docs/types",
+ "scripts": {},
+ "homepage": "https://github.com/stdlib-js/stdlib",
+ "repository": {
+ "type": "git",
+ "url": "git://github.com/stdlib-js/stdlib.git"
+ },
+ "bugs": {
+ "url": "https://github.com/stdlib-js/stdlib/issues"
+ },
+ "dependencies": {},
+ "devDependencies": {},
+ "engines": {
+ "node": ">=0.10.0",
+ "npm": ">2.7.0"
+ },
+ "os": [
+ "aix",
+ "darwin",
+ "freebsd",
+ "linux",
+ "macos",
+ "openbsd",
+ "sunos",
+ "win32",
+ "windows"
+ ],
+ "keywords": [
+ "stdlib",
+ "stdmath",
+ "statistics",
+ "stats",
+ "mathematics",
+ "math",
+ "covariance",
+ "sample covariance",
+ "variance",
+ "unbiased",
+ "var",
+ "deviation",
+ "dispersion",
+ "standard deviation",
+ "stdev",
+ "correlation",
+ "corr",
+ "incremental",
+ "accumulator",
+ "moving covariance",
+ "sliding window",
+ "sliding",
+ "window",
+ "moving"
+ ]
+}
diff --git a/lib/node_modules/@stdlib/stats/incr/nanmcovariance/test/test.js b/lib/node_modules/@stdlib/stats/incr/nanmcovariance/test/test.js
new file mode 100644
index 000000000000..ad7ad4aa3b0b
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmcovariance/test/test.js
@@ -0,0 +1,516 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 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 tape = require( 'tape' );
+var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' );
+var randu = require( '@stdlib/random/base/randu' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var zeros = require( '@stdlib/array/base/zeros' );
+var incrnanmcovariance = require( './../lib' );
+
+
+// FUNCTIONS //
+
+/**
+* Computes sample means using Welford's algorithm.
+*
+* @private
+* @param {Array} out - output array
+* @param {ArrayArray} arr - input array
+* @returns {Array} output array
+*/
+function mean( out, arr ) {
+ var delta;
+ var mx;
+ var my;
+ var N;
+ var i;
+
+ mx = 0.0;
+ my = 0.0;
+
+ N = 0;
+ for ( i = 0; i < arr.length; i++ ) {
+ N += 1;
+ delta = arr[i][0] - mx;
+ mx += delta / N;
+ delta = arr[i][1] - my;
+ my += delta / N;
+ }
+ out[ 0 ] = mx;
+ out[ 1 ] = my;
+ return out;
+}
+
+/**
+* Computes the covariance using textbook formula.
+*
+* @private
+* @param {ArrayArray} arr - input array
+* @param {number} mx - `x` mean
+* @param {number} my - `y` mean
+* @param {boolean} bool - boolean indicating whether to compute a biased covariance
+* @returns {number} covariance
+*/
+function covariance( arr, mx, my, bool ) {
+ var N;
+ var C;
+ var i;
+
+ N = arr.length;
+ C = 0.0;
+ for ( i = 0; i < N; i++ ) {
+ C += ( arr[i][0]-mx ) * ( arr[i][1]-my );
+ }
+ if ( bool ) {
+ return C / N;
+ }
+ if ( N === 1 ) {
+ return 0.0;
+ }
+ return C / (N-1);
+}
+
+/**
+* Generates a set of sample datasets.
+*
+* @private
+* @param {PositiveInteger} N - number of datasets
+* @param {PositiveInteger} M - dataset length
+* @param {PositiveInteger} [seed] - PRNG seed
+* @returns {ArrayArray} sample datasets
+*/
+function datasets( N, M, seed ) {
+ var data;
+ var rand;
+ var tmp;
+ var i;
+ var j;
+
+ rand = randu.factory({
+ 'seed': seed || ( randu()*pow( 2.0, 31 ) )|0
+ });
+
+ // Generate datasets consisting of (x,y) pairs of varying value ranges...
+ data = zeros( N );
+ for ( i = 0; i < N; i++ ) {
+ tmp = zeros( M );
+ for ( j = 0; j < M; j++ ) {
+ tmp[ j ] = [
+ rand() * pow( 10.0, i ),
+ rand() * pow( 10.0, i )
+ ];
+ }
+ data[ i ] = tmp;
+ }
+ return data;
+}
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+ t.ok( true, __filename );
+ t.strictEqual( typeof incrnanmcovariance, 'function', 'main export is a function' );
+ t.end();
+});
+
+tape( 'the function throws an error if not provided a positive integer for the window size', function test( t ) {
+ var values;
+ var i;
+
+ values = [
+ '5',
+ -5.0,
+ 0.0,
+ 3.14,
+ true,
+ null,
+ void 0,
+ NaN,
+ [],
+ {},
+ function noop() {}
+ ];
+
+ for ( i = 0; i < values.length; i++ ) {
+ t.throws( badValue( values[i] ), TypeError, 'throws an error when provided '+values[i] );
+ }
+ t.end();
+
+ function badValue( value ) {
+ return function badValue() {
+ incrnanmcovariance( value );
+ };
+ }
+});
+
+tape( 'the function throws an error if not provided a positive integer for the window size (known means)', function test( t ) {
+ var values;
+ var i;
+
+ values = [
+ '5',
+ -5.0,
+ 0.0,
+ 3.14,
+ true,
+ null,
+ void 0,
+ NaN,
+ [],
+ {},
+ function noop() {}
+ ];
+
+ for ( i = 0; i < values.length; i++ ) {
+ t.throws( badValue( values[i] ), TypeError, 'throws an error when provided '+values[i] );
+ }
+ t.end();
+
+ function badValue( value ) {
+ return function badValue() {
+ incrnanmcovariance( value, 3.0, 3.14 );
+ };
+ }
+});
+
+tape( 'the function throws an error if not provided a number as the mean value', function test( t ) {
+ var values;
+ var i;
+
+ values = [
+ '5',
+ true,
+ false,
+ null,
+ void 0,
+ [],
+ {},
+ function noop() {}
+ ];
+
+ for ( i = 0; i < values.length; i++ ) {
+ t.throws( badValue( values[i] ), TypeError, 'throws an error when provided '+values[i] );
+ }
+ t.end();
+
+ function badValue( value ) {
+ return function badValue() {
+ incrnanmcovariance( 3, value, 3.14 );
+ };
+ }
+});
+
+tape( 'the function throws an error if not provided a number as the mean value', function test( t ) {
+ var values;
+ var i;
+
+ values = [
+ '5',
+ true,
+ false,
+ null,
+ void 0,
+ [],
+ {},
+ function noop() {}
+ ];
+
+ for ( i = 0; i < values.length; i++ ) {
+ t.throws( badValue( values[i] ), TypeError, 'throws an error when provided '+values[i] );
+ }
+ t.end();
+
+ function badValue( value ) {
+ return function badValue() {
+ incrnanmcovariance( 3, 3.14, value );
+ };
+ }
+});
+
+tape( 'the function returns an accumulator function', function test( t ) {
+ t.strictEqual( typeof incrnanmcovariance( 3 ), 'function', 'returns expected value' );
+ t.end();
+});
+
+tape( 'the function returns an accumulator function (known means)', function test( t ) {
+ t.strictEqual( typeof incrnanmcovariance( 3, 3.0, 3.14 ), 'function', 'returns expected value' );
+ t.end();
+});
+
+tape( 'the accumulator function computes a moving unbiased sample covariance incrementally', function test( t ) {
+ var expected;
+ var actual;
+ var means;
+ var data;
+ var acc;
+ var arr;
+ var d;
+ var N;
+ var M;
+ var W;
+ var i;
+ var j;
+
+ N = 10;
+ M = 100;
+ data = datasets( N, M, 123456 );
+
+ // Define the window size:
+ W = 10;
+
+ // For each dataset, compute the actual and expected covariance...
+ for ( i = 0; i < N; i++ ) {
+ d = data[ i ];
+
+ acc = incrnanmcovariance( W );
+ for ( j = 0; j < M; j++ ) {
+ actual = acc( d[j][0], d[j][1] );
+ t.strictEqual( acc( NaN, d[j][1] ), actual, 'returns expected value' );
+ t.strictEqual( acc( d[j][0], NaN ), actual, 'returns expected value' );
+ if ( j < W ) {
+ arr = d.slice( 0, j+1 );
+ } else {
+ arr = d.slice( j-W+1, j+1 );
+ }
+ means = mean( [ 0.0, 0.0 ], arr );
+ expected = covariance( arr, means[ 0 ], means[ 1 ], false );
+ t.strictEqual( isAlmostSameValue( actual, expected, 8192 ), true, 'returns expected value' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the accumulator function computes a moving unbiased sample covariance incrementally (known means)', function test( t ) {
+ var expected;
+ var actual;
+ var means;
+ var data;
+ var acc;
+ var arr;
+ var d;
+ var N;
+ var M;
+ var W;
+ var i;
+ var j;
+
+ N = 10;
+ M = 100;
+ data = datasets( N, M, 123456 );
+
+ // Define the window size:
+ W = 10;
+
+ // For each dataset, compute the actual and expected covariance...
+ for ( i = 0; i < N; i++ ) {
+ d = data[ i ];
+ means = mean( [ 0.0, 0.0 ], d );
+ acc = incrnanmcovariance( W, means[ 0 ], means[ 1 ] );
+ for ( j = 0; j < M; j++ ) {
+ actual = acc( d[j][0], d[j][1] );
+ t.strictEqual( acc( NaN, d[j][1] ), actual, 'returns expected value' );
+ t.strictEqual( acc( d[j][0], NaN ), actual, 'returns expected value' );
+ if ( j < W ) {
+ arr = d.slice( 0, j+1 );
+ } else {
+ arr = d.slice( j-W+1, j+1 );
+ }
+ expected = covariance( arr, means[ 0 ], means[ 1 ], true );
+ t.strictEqual( isAlmostSameValue( actual, expected, 1674 ), true, 'returns expected value' );
+ }
+ }
+ t.end();
+});
+
+tape( 'if not provided an input value, the accumulator function returns the current unbiased sample covariance (unknown means)', function test( t ) {
+ var expected;
+ var actual;
+ var means;
+ var data;
+ var acc;
+ var W;
+ var N;
+ var d;
+ var i;
+
+ data = [
+ [ 2.0, 1.0 ],
+ [ -5.0, 3.14 ],
+ [ 3.0, -1.0 ],
+ [ 5.0, -9.5 ]
+ ];
+ N = data.length;
+
+ // Window size:
+ W = 3;
+
+ acc = incrnanmcovariance( W );
+ for ( i = 0; i < N; i++ ) {
+ acc( data[ i ][ 0 ], data[ i ][ 1 ] );
+ acc( NaN, data[ i ][ 1 ] );
+ acc( data[ i ][ 0 ], NaN );
+ actual = acc();
+ if ( i < W-1 ) {
+ d = data.slice( 0, i+1 );
+ } else {
+ d = data.slice( i-W+1, i+1 );
+ }
+ means = mean( [ 0.0, 0.0 ], d );
+ expected = covariance( d, means[ 0 ], means[ 1 ], false );
+ t.strictEqual( isAlmostSameValue( actual, expected, 2 ), true, 'returns expected value' );
+ }
+ t.end();
+});
+
+tape( 'if not provided an input value, the accumulator function returns the current unbiased sample covariance (known means)', function test( t ) {
+ var expected;
+ var actual;
+ var means;
+ var data;
+ var acc;
+ var W;
+ var N;
+ var d;
+ var i;
+
+ data = [
+ [ 2.0, 1.0 ],
+ [ -5.0, 3.14 ],
+ [ 3.0, -1.0 ],
+ [ 5.0, -9.5 ]
+ ];
+ N = data.length;
+ means = mean( [ 0.0, 0.0 ], data );
+
+ // Window size:
+ W = 3;
+
+ acc = incrnanmcovariance( W, means[ 0 ], means[ 1 ] );
+ for ( i = 0; i < N; i++ ) {
+ acc( data[ i ][ 0 ], data[ i ][ 1 ] );
+ acc( NaN, data[ i ][ 1 ] );
+ acc( data[ i ][ 0 ], NaN );
+ actual = acc();
+ if ( i < W-1 ) {
+ d = data.slice( 0, i+1 );
+ } else {
+ d = data.slice( i-W+1, i+1 );
+ }
+ expected = covariance( d, means[ 0 ], means[ 1 ], true );
+ t.strictEqual( isAlmostSameValue( actual, expected, 0 ), true, 'returns expected value' );
+ }
+ t.end();
+});
+
+tape( 'if data has yet to be provided, the accumulator function returns `null`', function test( t ) {
+ var acc = incrnanmcovariance( 3 );
+ t.strictEqual( acc(), null, 'returns expected value' );
+ t.end();
+});
+
+tape( 'if data has yet to be provided, the accumulator function returns `null` (known means)', function test( t ) {
+ var acc = incrnanmcovariance( 3, 3.0, 3.14 );
+ t.strictEqual( acc(), null, 'returns expected value' );
+ t.end();
+});
+
+tape( 'if only one datum has been provided and the means are unknown, the accumulator function returns `0`', function test( t ) {
+ var acc = incrnanmcovariance( 3 );
+ acc( 2.0, 3.14 );
+ t.strictEqual( acc(), 0.0, 'returns expected value' );
+ t.end();
+});
+
+tape( 'if only one datum has been provided and the means are known, the accumulator function may not return `0`', function test( t ) {
+ var acc = incrnanmcovariance( 3, 30.0, -100.0 );
+ acc( 2.0, 1.0 );
+ t.notEqual( acc(), 0.0, 'does not return 0' );
+ t.end();
+});
+
+tape( 'if the window size is `1` and the means are unknown, the accumulator function always returns `0`', function test( t ) {
+ var acc;
+ var cov;
+ var i;
+
+ acc = incrnanmcovariance( 1 );
+ for ( i = 0; i < 100; i++ ) {
+ cov = acc( randu()*100.0, randu()*100.0 );
+ t.strictEqual( cov, 0.0, 'returns expected value' );
+ }
+ t.end();
+});
+
+tape( 'if the window size is `1` and the means are known, the accumulator function may not always return `0`', function test( t ) {
+ var acc;
+ var cov;
+ var i;
+
+ acc = incrnanmcovariance( 1, 500.0, -500.0 ); // means are outside the range of simulated values so the covariance should never be zero
+ for ( i = 0; i < 100; i++ ) {
+ cov = acc( randu()*100.0, randu()*100.0 );
+ t.notEqual( cov, 0.0, 'does not return 0' );
+ }
+ t.end();
+});
+
+tape( 'if only `NaN` values have been provided, the accumulator function returns `null`', function test( t ) {
+ var acc = incrnanmcovariance( 3 );
+ acc( NaN, 1.0 );
+ acc( 1.0, NaN );
+ acc( NaN, NaN );
+ t.strictEqual( acc(), null, 'returns expected value' );
+ t.end();
+});
+
+tape( 'if only `NaN` values have been provided, the accumulator function returns `null` (known means)', function test( t ) {
+ var acc = incrnanmcovariance( 3, 3.0, 3.14 );
+ acc( NaN, 1.0 );
+ acc( 1.0, NaN );
+ acc( NaN, NaN );
+ t.strictEqual( acc(), null, 'returns expected value' );
+ t.end();
+});
+
+tape( 'if provided `NaN`, the accumulator function ignores the provided values and returns the current unbiased sample covariance', function test( t ) {
+ var acc = incrnanmcovariance( 3 );
+ t.strictEqual( acc( NaN, 1.0 ), null, 'returns expected value' );
+ t.strictEqual( acc( 1.0, 2.0 ), 0.0, 'returns expected value' );
+ t.strictEqual( acc( NaN, NaN ), 0.0, 'returns expected value' );
+ t.strictEqual( acc( 3.0, 6.0 ), 4.0, 'returns expected value' );
+ t.strictEqual( acc( 5.0, NaN ), 4.0, 'returns expected value' );
+ t.strictEqual( acc(), 4.0, 'returns expected value' );
+ t.end();
+});
+
+tape( 'if provided `NaN`, the accumulator function ignores the provided values and returns the current unbiased sample covariance (known means)', function test( t ) {
+ var acc = incrnanmcovariance( 3, 0.0, 0.0 );
+ t.strictEqual( acc( NaN, 1.0 ), null, 'returns expected value' );
+ t.strictEqual( acc( 1.0, 2.0 ), 2.0, 'returns expected value' );
+ t.strictEqual( acc( 1.0, NaN ), 2.0, 'returns expected value' );
+ t.strictEqual( acc( 2.0, 3.0 ), 4.0, 'returns expected value' );
+ t.strictEqual( acc( NaN, NaN ), 4.0, 'returns expected value' );
+ t.strictEqual( acc(), 4.0, 'returns expected value' );
+ t.end();
+});