diff --git a/lib/node_modules/@stdlib/stats/incr/nanmvariance/README.md b/lib/node_modules/@stdlib/stats/incr/nanmvariance/README.md
new file mode 100644
index 000000000000..6a5f7404c455
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmvariance/README.md
@@ -0,0 +1,183 @@
+
+
+# incrnanmvariance
+
+> Compute a moving [unbiased sample variance][sample-variance] incrementally, ignoring `NaN` values.
+
+
+
+For a window of size `W`, the [unbiased sample variance][sample-variance] is defined as
+
+
+
+```math
+s^2 = \frac{1}{W-1} \sum_{i=0}^{W-1} ( x_i - \bar{x} )^2
+```
+
+
+
+
+
+
+
+
+
+
+
+## Usage
+
+```javascript
+var incrnanmvariance = require( '@stdlib/stats/incr/nanmvariance' );
+```
+
+#### incrnanmvariance( window\[, mean] )
+
+Returns an accumulator `function` which incrementally computes a moving [unbiased sample variance][sample-variance]. The `window` parameter defines the number of values over which to compute the moving [unbiased sample variance][sample-variance], ignoring `NaN` values.
+
+```javascript
+var accumulator = incrnanmvariance( 3 );
+```
+
+If the mean is already known, provide a `mean` argument.
+
+```javascript
+var accumulator = incrnanmvariance( 3, 5.0 );
+```
+
+#### accumulator( \[x] )
+
+If provided an input value `x`, the accumulator function returns an updated [unbiased sample variance][sample-variance]. If not provided an input value `x` or provided a `NaN` value, the accumulator function returns the current [unbiased sample variance][sample-variance].
+
+```javascript
+var accumulator = incrnanmvariance( 3 );
+
+var s2 = accumulator();
+// returns null
+
+// Fill the window...
+s2 = accumulator( 2.0 ); // [2.0]
+// returns 0.0
+
+s2 = accumulator( 1.0 ); // [2.0, 1.0]
+// returns 0.5
+
+s2 = accumulator( NaN ); // [2.0, 1.0]
+// returns 0.5
+
+s2 = accumulator( 3.0 ); // [2.0, 1.0, 3.0]
+// returns 1.0
+
+// Window begins sliding...
+s2 = accumulator( -7.0 ); // [1.0, 3.0, -7.0]
+// returns 28.0
+
+s2 = accumulator( -5.0 ); // [3.0, -7.0, -5.0]
+// returns 28.0
+
+s2 = accumulator();
+// returns 28.0
+```
+
+
+
+
+
+
+
+## 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 `NaN` for **at least** `W-1` future invocations. 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` values 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 randu = require( '@stdlib/random/base/randu' );
+var incrnanmvariance = require( '@stdlib/stats/incr/nanmvariance' );
+
+var accumulator;
+var v;
+var i;
+
+// Initialize an accumulator:
+accumulator = incrnanmvariance( 5 );
+
+// For each simulated datum, update the moving unbiased sample variance...
+for ( i = 0; i < 100; i++ ) {
+ v = randu() * 100.0;
+ accumulator( v );
+}
+console.log( accumulator() );
+```
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+[sample-variance]: https://en.wikipedia.org/wiki/Variance
+
+
+
+[@stdlib/stats/incr/mmean]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/mmean
+
+[@stdlib/stats/incr/mstdev]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/mstdev
+
+[@stdlib/stats/incr/msummary]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/msummary
+
+[@stdlib/stats/incr/variance]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/variance
+
+
+
+
+
+
diff --git a/lib/node_modules/@stdlib/stats/incr/nanmvariance/benchmark/benchmark.js b/lib/node_modules/@stdlib/stats/incr/nanmvariance/benchmark/benchmark.js
new file mode 100644
index 000000000000..5d6350a81788
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmvariance/benchmark/benchmark.js
@@ -0,0 +1,92 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2018 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 incrnanmvariance = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+ var f;
+ var i;
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ f = incrnanmvariance( (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 = incrnanmvariance( 5 );
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ v = acc( 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_mean', pkg ), function benchmark( b ) {
+ var acc;
+ var v;
+ var i;
+
+ acc = incrnanmvariance( 5, 0.5 );
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ v = acc( 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/nanmvariance/docs/repl.txt b/lib/node_modules/@stdlib/stats/incr/nanmvariance/docs/repl.txt
new file mode 100644
index 000000000000..2d2f711b5729
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmvariance/docs/repl.txt
@@ -0,0 +1,51 @@
+
+{{alias}}( W[, mean] )
+ Returns an accumulator function which incrementally computes a moving
+ unbiased sample variance, ignoring `NaN` values.
+
+ The `W` parameter defines the number of values over which to compute the
+ moving unbiased sample variance.
+
+ If provided a value, the accumulator function returns an updated moving
+ unbiased sample variance. If not provided a value or provided a `NaN`
+ value, the accumulator function returns the current moving unbiased
+ sample variance.
+
+ As `W` values 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.
+
+ mean: number (optional)
+ Known mean.
+
+ Returns
+ -------
+ acc: Function
+ Accumulator function.
+
+ Examples
+ --------
+ > var accumulator = {{alias}}( 3 );
+ > var s2 = accumulator()
+ null
+ > s2 = accumulator( 2.0 )
+ 0.0
+ > s2 = accumulator( -5.0 )
+ 24.5
+ > s2 = accumulator( NaN )
+ 24.5
+ > s2 = accumulator( 3.0 )
+ 19.0
+ > s2 = accumulator( 5.0 )
+ 28.0
+ > s2 = accumulator()
+ 28.0
+
+ See Also
+ --------
+
diff --git a/lib/node_modules/@stdlib/stats/incr/nanmvariance/docs/types/index.d.ts b/lib/node_modules/@stdlib/stats/incr/nanmvariance/docs/types/index.d.ts
new file mode 100644
index 000000000000..e64caadc8529
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmvariance/docs/types/index.d.ts
@@ -0,0 +1,77 @@
+/*
+* @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 a value, returns an updated unbiased sample variance; otherwise, returns the current unbiased sample variance.
+*
+* ## Notes
+*
+* - If provided `NaN` value which, when used in computations, results in `NaN`, the accumulator returns the current unbiased variance.
+*
+* @param x - value
+* @returns unbiased sample variance
+*/
+type accumulator = ( x?: number ) => number | null;
+
+/**
+* Returns an accumulator function which incrementally computes a moving unbiased sample variance, ignoring `NaN` values.
+*
+* ## Notes
+*
+* - The `W` parameter defines the number of values over which to compute the moving unbiased sample variance.
+* - As `W` values 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 mean - mean value
+* @throws first argument must be a positive integer
+* @returns accumulator function
+*
+* @example
+* var accumulator = incrnanmvariance( 3 );
+*
+* var s2 = accumulator();
+* // returns null
+*
+* s2 = accumulator( 2.0 );
+* // returns 0.0
+*
+* s2 = accumulator( -5.0 );
+* // returns 24.5
+*
+* s2 = accumulator( 3.0 );
+* // returns 19.0
+*
+* s2 = accumulator( 5.0 );
+* // returns 28.0
+*
+* s2 = accumulator();
+* // returns 28.0
+*
+* @example
+* var accumulator = incrnanmvariance( 3, -2.0 );
+*/
+declare function incrnanmvariance( W: number, mean?: number ): accumulator;
+
+
+// EXPORTS //
+
+export = incrnanmvariance;
diff --git a/lib/node_modules/@stdlib/stats/incr/nanmvariance/docs/types/test.ts b/lib/node_modules/@stdlib/stats/incr/nanmvariance/docs/types/test.ts
new file mode 100644
index 000000000000..ff12831b1236
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmvariance/docs/types/test.ts
@@ -0,0 +1,77 @@
+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2019 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 incrnanmvariance = require( './index' );
+
+
+// TESTS //
+
+// The function returns an accumulator function...
+{
+ incrnanmvariance( 3 ); // $ExpectType accumulator
+ incrnanmvariance( 3, 0.0 ); // $ExpectType accumulator
+}
+
+// The compiler throws an error if the function is provided a first argument which is not a number...
+{
+ incrnanmvariance( '5' ); // $ExpectError
+ incrnanmvariance( true ); // $ExpectError
+ incrnanmvariance( false ); // $ExpectError
+ incrnanmvariance( null ); // $ExpectError
+ incrnanmvariance( [] ); // $ExpectError
+ incrnanmvariance( {} ); // $ExpectError
+ incrnanmvariance( ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a second argument which is not a number...
+{
+ incrnanmvariance( 3, '5' ); // $ExpectError
+ incrmvariance( 3, true ); // $ExpectError
+ incrnanmvariance( 3, false ); // $ExpectError
+ incrnanmvariance( 3, null ); // $ExpectError
+ incrnanmvariance( 3, [] ); // $ExpectError
+ incrnanmvariance( 3, {} ); // $ExpectError
+ incrnanmvariance( 3, ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided an invalid number of arguments...
+{
+ incrnanmvariance(); // $ExpectError
+ incrnanmvariance( 3, 2.5, 3 ); // $ExpectError
+}
+
+// The function returns an accumulator function which returns an accumulated result...
+{
+ const acc = incrnanmvariance( 3 );
+
+ acc(); // $ExpectType number | null
+ acc( 3.14 ); // $ExpectType number | null
+}
+
+// The compiler throws an error if the returned accumulator function is provided invalid arguments...
+{
+ const acc = incrnanmvariance( 3 );
+
+ acc( '5' ); // $ExpectError
+ acc( true ); // $ExpectError
+ acc( false ); // $ExpectError
+ acc( null ); // $ExpectError
+ acc( [] ); // $ExpectError
+ acc( {} ); // $ExpectError
+ acc( ( x: number ): number => x ); // $ExpectError
+}
diff --git a/lib/node_modules/@stdlib/stats/incr/nanmvariance/examples/index.js b/lib/node_modules/@stdlib/stats/incr/nanmvariance/examples/index.js
new file mode 100644
index 000000000000..77aa13bbb096
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmvariance/examples/index.js
@@ -0,0 +1,38 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2018 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 randu = require( '@stdlib/random/base/randu' );
+var incrnanmvariance = require( './../lib' );
+
+var accumulator;
+var s2;
+var v;
+var i;
+
+// Initialize an accumulator:
+accumulator = incrnanmvariance( 5 );
+
+// For each simulated datum, update the moving unbiased sample variance ignoring `NaN` values...
+console.log( '\nValue\tSample Variance\n' );
+for ( i = 0; i < 100; i++ ) {
+ v = randu() * 100.0;
+ s2 = accumulator( v );
+ console.log( '%d\t%d', v.toFixed( 4 ), s2.toFixed( 4 ) );
+}
diff --git a/lib/node_modules/@stdlib/stats/incr/nanmvariance/lib/index.js b/lib/node_modules/@stdlib/stats/incr/nanmvariance/lib/index.js
new file mode 100644
index 000000000000..000f371854f0
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmvariance/lib/index.js
@@ -0,0 +1,60 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2018 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 variance incrementally, ignoring `NaN` values.
+*
+* @module @stdlib/stats/incr/nanmvariance
+*
+* @example
+* var incrnanmvariance = require( '@stdlib/stats/incr/nanmvariance' );
+*
+* var accumulator = incrnanmvariance( 3 );
+*
+* var s2 = accumulator();
+* // returns null
+*
+* s2 = accumulator( 2.0 );
+* // returns 0.0
+*
+* s2 = accumulator( -5.0 );
+* // returns 24.5
+*
+* s2 = accumulator( NaN );
+* // returns 24.5
+*
+* s2 = accumulator( 3.0 );
+* // returns 19.0
+*
+* s2 = accumulator( 5.0 );
+* // returns 28.0
+*
+* s2 = accumulator();
+* // returns 28.0
+*/
+
+// MODULES //
+
+var main = require( './main.js' );
+
+
+// EXPORTS //
+
+module.exports = main;
diff --git a/lib/node_modules/@stdlib/stats/incr/nanmvariance/lib/main.js b/lib/node_modules/@stdlib/stats/incr/nanmvariance/lib/main.js
new file mode 100644
index 000000000000..028d6f93f957
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmvariance/lib/main.js
@@ -0,0 +1,93 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2018 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 incrmvariance = require( '@stdlib/stats/incr/mvariance' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+
+
+// MAIN //
+
+/**
+* Returns an accumulator function which incrementally computes a moving unbiased sample variance, ignoring `NaN` values.
+*
+* @param {PositiveInteger} W - window size
+* @param {number} [mean] - mean value
+* @throws {TypeError} first argument must be a positive integer
+* @throws {TypeError} second argument must be a number
+* @returns {Function} accumulator function
+*
+* @example
+* var accumulator = incrnanmvariance( 3 );
+*
+* var s2 = accumulator();
+* // returns null
+*
+* s2 = accumulator( 2.0 );
+* // returns 0.0
+*
+* s2 = accumulator( -5.0 );
+* // returns 24.5
+*
+* s2 = accumulator( NaN );
+* // returns 24.5
+*
+* s2 = accumulator( 3.0 );
+* // returns 19.0
+*
+* s2 = accumulator( 5.0 );
+* // returns 28.0
+*
+* s2 = accumulator();
+* // returns 28.0
+*
+* @example
+* var accumulator = incrnanmvariance( 3, -2.0 );
+*/
+function incrnanmvariance( W, mean ) {
+ var acc;
+
+ if ( arguments.length > 1 ) {
+ acc = incrmvariance( W, mean );
+ } else {
+ acc = incrmvariance( W );
+ }
+ return accumulator;
+
+ /**
+ * If provided a value, returns an updated unbiased sample variance. If not provided a value or provided a `NaN` value, returns the current unbiased sample variance.
+ *
+ * @private
+ * @param {number} [x] - input value
+ * @returns {(number|null)} unbiased sample variance or null
+ */
+ function accumulator( x ) {
+ if ( arguments.length === 0 || isnan( x ) ) {
+ return acc();
+ }
+ return acc( x );
+ }
+}
+
+
+// EXPORTS //
+
+module.exports = incrnanmvariance;
diff --git a/lib/node_modules/@stdlib/stats/incr/nanmvariance/package.json b/lib/node_modules/@stdlib/stats/incr/nanmvariance/package.json
new file mode 100644
index 000000000000..4ec4f178a2e1
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmvariance/package.json
@@ -0,0 +1,76 @@
+{
+ "name": "@stdlib/stats/incr/nanmvariance",
+ "version": "0.0.0",
+ "description": "Compute a moving unbiased sample variance 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",
+ "variance",
+ "sample",
+ "sample variance",
+ "unbiased",
+ "stdev",
+ "standard",
+ "deviation",
+ "dispersion",
+ "incremental",
+ "accumulator",
+ "moving variance",
+ "sliding window",
+ "sliding",
+ "window",
+ "moving",
+ "nan",
+ "ignore"
+ ]
+}
diff --git a/lib/node_modules/@stdlib/stats/incr/nanmvariance/test/test.js b/lib/node_modules/@stdlib/stats/incr/nanmvariance/test/test.js
new file mode 100644
index 000000000000..57ebd2104575
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmvariance/test/test.js
@@ -0,0 +1,531 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2018 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 randu = require( '@stdlib/random/base/randu' );
+var abs = require( '@stdlib/math/base/special/abs' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+var zeros = require( '@stdlib/array/base/zeros' );
+var incrnanmvariance = require( './../lib' );
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+ t.ok( true, __filename );
+ t.strictEqual( typeof incrnanmvariance, '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() {
+ incrnanmvariance( value );
+ };
+ }
+});
+
+tape( 'the function throws an error if not provided a positive integer for the window size (known mean)', 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() {
+ incrnanmvariance( value, 3.0 );
+ };
+ }
+});
+
+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() {
+ incrnanmvariance( 3, value );
+ };
+ }
+});
+
+tape( 'the function returns an accumulator function', function test( t ) {
+ t.strictEqual( typeof incrnanmvariance( 3 ), 'function', 'returns expected value' );
+ t.end();
+});
+
+tape( 'the function returns an accumulator function (known mean)', function test( t ) {
+ t.strictEqual( typeof incrnanmvariance( 3, 3.0 ), 'function', 'returns expected value' );
+ t.end();
+});
+
+tape( 'the accumulator function computes a moving unbiased sample variance incrementally', function test( t ) {
+ var expected;
+ var actual;
+ var data;
+ var acc;
+ var N;
+ var i;
+
+ data = [ 2.0, 3.0, 4.0, -1.0, 3.0, 1.0 ];
+ N = data.length;
+
+ acc = incrnanmvariance( 3 );
+
+ actual = zeros( N );
+ for ( i = 0; i < N; i++ ) {
+ actual[ i ] = acc( data[ i ] );
+ }
+ expected = [ 0.0, 0.5, 1.0, 7.0, 7.0, 4.0 ];
+
+ t.deepEqual( actual, expected, 'returns expected incremental results' );
+ t.end();
+});
+
+tape( 'the accumulator function computes a moving unbiased sample variance incrementally (known mean)', function test( t ) {
+ var expected;
+ var actual;
+ var data;
+ var acc;
+ var N;
+ var i;
+
+ data = [ 2.0, 3.0, 4.0, -1.0, 3.0, 1.0 ];
+ N = data.length;
+
+ acc = incrnanmvariance( 3, 2.0 );
+
+ actual = zeros( N );
+ for ( i = 0; i < N; i++ ) {
+ actual[ i ] = acc( data[ i ] );
+ }
+ expected = [
+ 0.0,
+ 0.5,
+ 1.6666666666666667,
+ 4.666666666666667,
+ 4.666666666666667,
+ 3.6666666666666665
+ ];
+
+ t.deepEqual( actual, expected, 'returns expected incremental results' );
+ t.end();
+});
+
+tape( 'if not provided an input value, the accumulator function returns the current unbiased sample variance', function test( t ) {
+ var expected;
+ var actual;
+ var delta;
+ var data;
+ var tol;
+ var acc;
+ var i;
+
+ data = [ 2.0, 3.0, 10.0 ];
+ acc = incrnanmvariance( 3 );
+ for ( i = 0; i < data.length-1; i++ ) {
+ acc( data[ i ] );
+ }
+ t.strictEqual( acc(), 0.5, 'returns current unbiased sample variance' );
+
+ acc( data[ data.length-1 ] );
+
+ expected = 19.0;
+ actual = acc();
+ delta = abs( actual - expected );
+ tol = EPS * expected;
+
+ t.strictEqual( delta < tol, true, 'expected: '+expected+'. actual: '+actual+'. tol: '+tol+'. delta: '+delta+'.' );
+ t.end();
+});
+
+tape( 'if not provided an input value, the accumulator function returns the current unbiased sample variance (known mean)', function test( t ) {
+ var expected;
+ var actual;
+ var delta;
+ var data;
+ var tol;
+ var acc;
+ var i;
+
+ data = [ 2.0, 3.0, 10.0 ];
+ acc = incrnanmvariance( 3, 5.0 );
+ for ( i = 0; i < data.length-1; i++ ) {
+ acc( data[ i ] );
+ }
+ t.strictEqual( acc(), 6.5, 'returns current unbiased sample variance' );
+
+ acc( data[ data.length-1 ] );
+
+ expected = 12.666666666666666;
+ actual = acc();
+ delta = abs( actual - expected );
+ tol = EPS * expected;
+
+ t.strictEqual( delta < tol, true, 'expected: '+expected+'. actual: '+actual+'. tol: '+tol+'. delta: '+delta+'.' );
+ t.end();
+});
+
+tape( 'if data has yet to be provided, the accumulator function returns `null`', function test( t ) {
+ var acc = incrnanmvariance( 3 );
+ t.strictEqual( acc(), null, 'returns expected value' );
+ t.end();
+});
+
+tape( 'if data has yet to be provided, the accumulator function returns `null` (known mean)', function test( t ) {
+ var acc = incrnanmvariance( 3, 3.0 );
+ t.strictEqual( acc(), null, 'returns expected value' );
+ t.end();
+});
+
+tape( 'if only one datum has been provided and the mean is unknown, the accumulator function returns `0`', function test( t ) {
+ var acc = incrnanmvariance( 3 );
+ acc( 2.0 );
+ t.strictEqual( acc(), 0.0, 'returns expected value' );
+ t.end();
+});
+
+tape( 'if only one datum has been provided and the mean is known, the accumulator function may not return `0`', function test( t ) {
+ var acc = incrnanmvariance( 3, 30 );
+ acc( 2.0 );
+ t.notEqual( acc(), 0.0, 'does not return 0' );
+ t.end();
+});
+
+tape( 'if the window size is `1` and the mean is unknown, the accumulator function always returns `0`', function test( t ) {
+ var acc;
+ var s2;
+ var i;
+
+ acc = incrnanmvariance( 1 );
+ for ( i = 0; i < 100; i++ ) {
+ s2 = acc( randu() * 100.0 );
+ t.strictEqual( s2, 0.0, 'returns expected value' );
+ }
+ t.end();
+});
+
+tape( 'if the window size is `1` and the mean is known, the accumulator function may not always return `0`', function test( t ) {
+ var acc;
+ var s2;
+ var i;
+
+ acc = incrnanmvariance( 1, 500.0 ); // mean is outside the range of simulated values so the variance should never be zero
+ for ( i = 0; i < 100; i++ ) {
+ s2 = acc( randu() * 100.0 );
+ t.notEqual( s2, 0.0, 'does not return 0' );
+ }
+ t.end();
+});
+
+tape( 'if provided `NaN`, the currently accumulated value is returned (unknown mean)', function test( t ) {
+ var expected;
+ var data;
+ var acc;
+ var v;
+ var i;
+
+ acc = incrnanmvariance( 3 );
+
+ data = [
+ NaN,
+ 3.14, // 3.14
+ 3.14, // 3.14, 3.14
+ NaN, // 3.14, 3.14
+ 3.14, // 3.14, 3.14, 3.14
+ 3.14, // 3.14, 3.14, 3.14
+ 3.14, // 3.14, 3.14, 3.14
+ NaN, // 3.14, 3.14, 3.14
+ 3.14, // 3.14, 3.14, 3.14
+ 3.14, // 3.14, 3.14, 3.14
+ 3.14, // 3.14, 3.14, 3.14
+ NaN, // 3.14, 3.14, 3.14
+ 3.14, // 3.14, 3.14, 3.14
+ 3.14, // 3.14, 3.14, 3.14
+ NaN, // 3.14, 3.14, 3.14
+ NaN, // 3.14, 3.14, 3.14
+ NaN, // 3.14, 3.14, 3.14
+ NaN, // 3.14, 3.14, 3.14
+ 3.14 // 3.14, 3.14, 3.14
+ ];
+ expected = [
+ null,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0
+ ];
+ for ( i = 0; i < data.length; i++ ) {
+ v = acc( data[ i ] );
+ t.strictEqual( v, expected[ i ], 'returns expected value for window '+i );
+ t.strictEqual( acc(), expected[ i ], 'returns expected value for window '+i );
+ }
+ t.end();
+});
+
+tape( 'if provided `NaN`, the currently accumulated value is returned (known mean)', function test( t ) {
+ var expected;
+ var data;
+ var acc;
+ var v;
+ var i;
+
+ acc = incrnanmvariance( 3, 3.14 );
+
+ data = [
+ NaN,
+ 3.14, // 3.14
+ 3.14, // 3.14, 3.14
+ NaN, // 3.14, 3.14
+ 3.14, // 3.14, 3.14, 3.14
+ 3.14, // 3.14, 3.14, 3.14
+ 3.14, // 3.14, 3.14, 3.14
+ NaN, // 3.14, 3.14, 3.14
+ 3.14, // 3.14, 3.14, 3.14
+ 3.14, // 3.14, 3.14, 3.14
+ 3.14, // 3.14, 3.14, 3.14
+ NaN, // 3.14, 3.14, 3.14
+ 3.14, // 3.14, 3.14, 3.14
+ 3.14, // 3.14, 3.14, 3.14
+ NaN, // 3.14, 3.14, 3.14
+ NaN, // 3.14, 3.14, 3.14
+ NaN, // 3.14, 3.14, 3.14
+ NaN, // 3.14, 3.14, 3.14
+ 3.14 // 3.14, 3.14, 3.14
+ ];
+ expected = [
+ null,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0
+ ];
+
+ for ( i = 0; i < data.length; i++ ) {
+ v = acc( data[ i ] );
+ t.strictEqual( v, expected[ i ], 'returns expected value for window '+i );
+ t.strictEqual( acc(), expected[ i ], 'returns expected value for window '+i );
+ }
+ t.end();
+});
+
+tape( 'if provided `NaN`, the currently accumulated value returned (unknown mean, W=1)', function test( t ) {
+ var expected;
+ var data;
+ var acc;
+ var v;
+ var i;
+
+ acc = incrnanmvariance( 1 );
+
+ data = [
+ NaN,
+ 3.14,
+ 3.14,
+ NaN,
+ 3.14,
+ 3.14,
+ 3.14,
+ NaN,
+ 3.14,
+ 3.14,
+ 3.14,
+ NaN,
+ 3.14,
+ 3.14,
+ NaN,
+ NaN,
+ NaN,
+ NaN,
+ 3.14
+ ];
+ expected = [
+ null,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0
+ ];
+
+ for ( i = 0; i < data.length; i++ ) {
+ v = acc( data[ i ] );
+ t.strictEqual( v, expected[ i ], 'returns expected value for window '+i );
+ t.strictEqual( acc(), expected[ i ], 'returns expected value for window '+i );
+ }
+ t.end();
+});
+
+tape( 'if provided `NaN`, the currently accumulated value returned (known mean)', function test( t ) {
+ var expected;
+ var data;
+ var acc;
+ var v;
+ var i;
+
+ acc = incrnanmvariance( 1, 3.14 );
+
+ data = [
+ NaN,
+ 3.14,
+ 3.14,
+ NaN,
+ 3.14,
+ 3.14,
+ 3.14,
+ NaN,
+ 3.14,
+ 3.14,
+ 3.14,
+ NaN,
+ 3.14,
+ 3.14,
+ NaN,
+ NaN,
+ NaN,
+ NaN,
+ 3.14
+ ];
+ expected = [
+ null,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0,
+ 0.0
+ ];
+ for ( i = 0; i < data.length; i++ ) {
+ v = acc( data[ i ] );
+ t.strictEqual( v, expected[ i ], 'returns expected value for window '+i );
+ t.strictEqual( acc(), expected[ i ], 'returns expected value for window '+i );
+ }
+ t.end();
+});