From 644a4614d12542a05b847397faeebde5961160c3 Mon Sep 17 00:00:00 2001
From: gururaj1512 <gururajgurram1512@gmail.com>
Date: Sat, 19 Jul 2025 19:05:10 +0000
Subject: [PATCH 1/3] feat: add `stats/base/ndarray/ztest2`

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---
 .../stats/base/ndarray/ztest2/README.md       | 185 +++++++++
 .../ndarray/ztest2/benchmark/benchmark.js     | 128 +++++++
 .../stats/base/ndarray/ztest2/docs/repl.txt   |  68 ++++
 .../base/ndarray/ztest2/docs/types/index.d.ts |  92 +++++
 .../base/ndarray/ztest2/docs/types/test.ts    |  57 +++
 .../base/ndarray/ztest2/examples/index.js     |  64 ++++
 .../stats/base/ndarray/ztest2/lib/index.js    |  78 ++++
 .../stats/base/ndarray/ztest2/lib/main.js     | 123 ++++++
 .../stats/base/ndarray/ztest2/package.json    |  65 ++++
 .../stats/base/ndarray/ztest2/test/test.js    | 352 ++++++++++++++++++
 10 files changed, 1212 insertions(+)
 create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/ztest2/README.md
 create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/ztest2/benchmark/benchmark.js
 create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/ztest2/docs/repl.txt
 create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/ztest2/docs/types/index.d.ts
 create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/ztest2/docs/types/test.ts
 create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/ztest2/examples/index.js
 create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/ztest2/lib/index.js
 create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/ztest2/lib/main.js
 create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/ztest2/package.json
 create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/ztest2/test/test.js

diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/README.md b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/README.md
new file mode 100644
index 000000000000..69ee6d503b8b
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/README.md
@@ -0,0 +1,185 @@
+<!--
+
+@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.
+
+-->
+
+# ztest2
+
+> Compute a two-sample Z-test for two one-dimensional ndarrays.
+
+<section class="intro">
+
+A Z-test commonly refers to a two-sample location test which compares the means of two independent sets of measurements `X` and `Y` when the population standard deviations are known. A Z-test supports testing three different null hypotheses `H0`:
+
+-   `H0: μX - μY ≥ Δ` versus the alternative hypothesis `H1: μX - μY < Δ`.
+-   `H0: μX - μY ≤ Δ` versus the alternative hypothesis `H1: μX - μY > Δ`.
+-   `H0: μX - μY = Δ` versus the alternative hypothesis `H1: μX - μY ≠ Δ`.
+
+Here, `μX` and `μY` are the true population means of samples `X` and `Y`, respectively, and `Δ` is the hypothesized difference in means (typically `0` by default).
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var ztest2 = require( '@stdlib/stats/base/ndarray/ztest2' );
+```
+
+#### ztest2( arrays )
+
+Computes a two-sample Z-test for two one-dimensional ndarrays.
+
+```javascript
+var Float64Results = require( '@stdlib/stats/base/ztest/two-sample/results/float64' );
+var resolveEnum = require( '@stdlib/stats/base/ztest/alternative-resolve-enum' );
+var structFactory = require( '@stdlib/array/struct-factory' );
+var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+var ndarray = require( '@stdlib/ndarray/ctor' );
+
+var opts = {
+    'dtype': 'generic'
+};
+
+var xbuf = [ 4.0, 4.0, 6.0, 6.0, 5.0 ];
+var x = new ndarray( opts.dtype, xbuf, [ 5 ], [ 1 ], 0, 'row-major' );
+
+var ybuf = [ 3.0, 3.0, 5.0, 7.0, 7.0 ];
+var y = new ndarray( opts.dtype, ybuf, [ 5 ], [ 1 ], 0, 'row-major' );
+
+var alt = scalar2ndarray( resolveEnum( 'two-sided' ), {
+    'dtype': 'int8'
+});
+var alpha = scalar2ndarray( 0.05, opts );
+var diff = scalar2ndarray( 0.0, opts );
+var sigmax = scalar2ndarray( 1.0, opts );
+var sigmay = scalar2ndarray( 2.0, opts );
+
+var ResultsArray = structFactory( Float64Results );
+var out = new ndarray( Float64Results, new ResultsArray( 1 ), [], [ 0 ], 0, 'row-major' );
+
+var v = ztest2( [ x, y, out, alt, alpha, diff, sigmax, sigmay ] );
+
+var bool = ( v === out );
+// returns true
+```
+
+The function has the following parameters:
+
+-   **arrays**: array-like object containing the following ndarrays in order:
+
+    1.  first one-dimensional input ndarray.
+    1.  second one-dimensional input ndarray.
+    2.  a zero-dimensional output ndarray containing a [results object][@stdlib/stats/base/ztest/two-sample/results/float64].
+    3.  a zero-dimensional ndarray specifying the alternative hypothesis.
+    4.  a zero-dimensional ndarray specifying the significance level.
+    5.  a zero-dimensional ndarray specifying the difference in means under the null hypothesis.
+    6.  a zero-dimensional ndarray specifying the known standard deviation of first one-dimensional input ndarray.
+    7.  a zero-dimensional ndarray specifying the known standard deviation of second one-dimensional input ndarray.
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   As a general rule of thumb, a Z-test is most reliable for sample sizes greater than `50`. For smaller sample sizes or when the standard deviation is unknown, prefer a t-test.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Float64Results = require( '@stdlib/stats/base/ztest/two-sample/results/float64' );
+var resolveEnum = require( '@stdlib/stats/base/ztest/alternative-resolve-enum' );
+var structFactory = require( '@stdlib/array/struct-factory' );
+var normal = require( '@stdlib/random/array/normal' );
+var ndarray = require( '@stdlib/ndarray/ctor' );
+var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+var ndarray2array = require( '@stdlib/ndarray/to-array' );
+var ztest2 = require( '@stdlib/stats/base/ndarray/ztest2' );
+
+var opts = {
+    'dtype': 'generic'
+};
+
+// Create a one-dimensional ndarrays containing pseudorandom numbers drawn from a normal distribution:
+var xbuf = normal( 100, 0.0, 1.0, opts );
+var x = new ndarray( opts.dtype, xbuf, [ xbuf.length ], [ 1 ], 0, 'row-major' );
+console.log( ndarray2array( x ) );
+
+var ybuf = normal( 100, 0.0, 1.0, opts );
+var y = new ndarray( opts.dtype, ybuf, [ ybuf.length ], [ 1 ], 0, 'row-major' );
+console.log( ndarray2array( y ) );
+
+// Specify the alternative hypothesis:
+var alt = scalar2ndarray( resolveEnum( 'two-sided' ), {
+    'dtype': 'int8'
+});
+
+// Specify the significance level:
+var alpha = scalar2ndarray( 0.05, opts );
+
+// Specify the difference in means under the null hypothesis:
+var diff = scalar2ndarray( 0.0, opts );
+
+// Specify the known standard deviations:
+var sigmax = scalar2ndarray( 1.0, opts );
+var sigmay = scalar2ndarray( 1.0, opts );
+
+// Create a zero-dimensional results ndarray:
+var ResultsArray = structFactory( Float64Results );
+var out = new ndarray( Float64Results, new ResultsArray( 1 ), [], [ 0 ], 0, 'row-major' );
+
+// Perform a Z-test:
+var v = ztest2( [ x, y, out, alt, alpha, diff, sigmax, sigmay ] );
+console.log( v.get().toString() );
+```
+
+</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">
+
+[@stdlib/stats/base/ztest/two-sample/results/float64]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/base/ztest/two-sample/results/float64
+
+</section>
+
+<!-- /.links -->
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/benchmark/benchmark.js b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/benchmark/benchmark.js
new file mode 100644
index 000000000000..b932b1e371b8
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/benchmark/benchmark.js
@@ -0,0 +1,128 @@
+/**
+* @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 normal = require( '@stdlib/random/array/normal' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var ndarray = require( '@stdlib/ndarray/base/ctor' );
+var scalar2ndarray = require( '@stdlib/ndarray/base/from-scalar' );
+var Float64Results = require( '@stdlib/stats/base/ztest/two-sample/results/float64' );
+var resolveEnum = require( '@stdlib/stats/base/ztest/alternative-resolve-enum' );
+var structFactory = require( '@stdlib/array/struct-factory' );
+var pkg = require( './../package.json' ).name;
+var ztest2 = require( './../lib' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'generic'
+};
+var ResultsArray = structFactory( Float64Results );
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} len - array length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( len ) {
+	var sigmax;
+	var sigmay;
+	var alpha;
+	var diff;
+	var xbuf;
+	var ybuf;
+	var obuf;
+	var out;
+	var alt;
+	var x;
+	var y;
+
+	xbuf = normal( len, 0.0, 1.0, options );
+	x = new ndarray( options.dtype, xbuf, [ len ], [ 1 ], 0, 'row-major' );
+
+	ybuf = normal( len, 0.0, 1.0, options );
+	y = new ndarray( options.dtype, ybuf, [ len ], [ 1 ], 0, 'row-major' );
+
+	obuf = new ResultsArray( 1 );
+	out = new ndarray( Float64Results, obuf, [], [ 0 ], 0, 'row-major' );
+
+	alt = scalar2ndarray( resolveEnum( 'two-sided' ), 'int8', 'row-major' );
+	alpha = scalar2ndarray( 0.05, options.dtype, 'row-major' );
+	diff = scalar2ndarray( 0.0, options.dtype, 'row-major' );
+	sigmax = scalar2ndarray( 1.0, options.dtype, 'row-major' );
+	sigmay = scalar2ndarray( 1.0, options.dtype, 'row-major' );
+
+	return benchmark;
+
+	function benchmark( b ) {
+		var v;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			v = ztest2( [ x, y, out, alt, alpha, diff, sigmax, sigmay ] );
+			if ( typeof v !== 'object' ) {
+				b.fail( 'should return an ndarray' );
+			}
+		}
+		b.toc();
+		if ( isnan( v.get().statistic ) || isnan( v.get().pValue ) ) {
+			b.fail( 'should not return NaN' );
+		}
+		b.pass( 'benchmark finished' );
+		b.end();
+	}
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+	var len;
+	var min;
+	var max;
+	var f;
+	var i;
+
+	min = 1; // 10^min
+	max = 6; // 10^max
+
+	for ( i = min; i <= max; i++ ) {
+		len = pow( 10, i );
+		f = createBenchmark( len );
+		bench( pkg+':len='+len, f );
+	}
+}
+
+main();
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/docs/repl.txt b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/docs/repl.txt
new file mode 100644
index 000000000000..13050aad8a6b
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/docs/repl.txt
@@ -0,0 +1,68 @@
+
+{{alias}}( arrays )
+    Computes a two-sample Z-test for two one-dimensional ndarrays.
+
+    Parameters
+    ----------
+    arrays: ArrayLikeObject<ndarray>
+        Array-like object containing the following ndarrays in order:
+
+        - first one-dimensional input ndarray.
+        - second one-dimensional input ndarray.
+        - a zero-dimensional output ndarray containing a results object.
+        - a zero-dimensional ndarray specifying the alternative hypothesis.
+        - a zero-dimensional ndarray specifying the significance level.
+        - a zero-dimensional ndarray specifying the difference in means under
+        the null hypothesis.
+        - a zero-dimensional ndarray specifying the known standard deviation of
+        first one-dimensional input ndarray.
+        - a zero-dimensional ndarray specifying the known standard deviation of
+        second one-dimensional input ndarray.
+
+    Returns
+    -------
+    out: ndarray
+        Output ndarray.
+
+    Examples
+    --------
+    // Create the input ndarray:
+    > var xbuf = [ 4.0, 4.0, 6.0, 6.0, 5.0 ];
+    > var ybuf = [ 3.0, 3.0, 5.0, 7.0, 7.0 ];
+    > var dt = 'generic';
+    > var sh = [ xbuf.length ];
+    > var st = [ 1 ];
+    > var oo = 0;
+    > var ord = 'row-major';
+    > var x = new {{alias:@stdlib/ndarray/ctor}}( dt, xbuf, sh, st, oo, ord );
+    > var y = new {{alias:@stdlib/ndarray/ctor}}( dt, ybuf, sh, st, oo, ord );
+
+    // Create the output ndarray:
+    > var S = {{alias:@stdlib/stats/base/ztest/two-sample/results/float64}};
+    > var Results = {{alias:@stdlib/array/struct-factory}}( S );
+    > var obuf = new Results( 1 );
+    > var out = new {{alias:@stdlib/ndarray/ctor}}( S, obuf, [], [ 0 ], 0, ord );
+
+    // Specify the alternative hypothesis:
+    > var alt = {{alias:@stdlib/ndarray/from-scalar}}( 'two-sided' );
+
+    // Specify the significance level:
+    > var opts = { 'dtype': dt };
+    > var alpha = {{alias:@stdlib/ndarray/from-scalar}}( 0.05, opts );
+
+    // Specify the difference in means under the null hypothesis:
+    > var diff = {{alias:@stdlib/ndarray/from-scalar}}( 0.0, opts );
+
+    // Specify the known standard deviations:
+    > var sigmax = {{alias:@stdlib/ndarray/from-scalar}}( 1.0, opts );
+    > var sigmay = {{alias:@stdlib/ndarray/from-scalar}}( 2.0, opts );
+
+    // Perform a Z-test:
+    > {{alias}}( [ x, y, out, alt, alpha, diff, sigmax, sigmay ] );
+
+    // Print the results:
+    > out.get().toString()
+
+    See Also
+    --------
+
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/docs/types/index.d.ts b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/docs/types/index.d.ts
new file mode 100644
index 000000000000..2563ce3caf5c
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/docs/types/index.d.ts
@@ -0,0 +1,92 @@
+/*
+* @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.
+*/
+
+// TypeScript Version: 4.1
+
+/// <reference types="@stdlib/types"/>
+
+import { typedndarray, ndarray } from '@stdlib/types/ndarray';
+
+/**
+* Computes a two-sample Z-test for two one-dimensional ndarrays.
+*
+* ## Notes
+*
+* -   The function expects the following ndarrays in order:
+*
+*     -   first one-dimensional input ndarray.
+*     -   second one-dimensional input ndarray.
+*     -   a zero-dimensional output ndarray containing a results object.
+*     -   a zero-dimensional ndarray specifying the alternative hypothesis.
+*     -   a zero-dimensional ndarray specifying the significance level.
+*     -   a zero-dimensional ndarray specifying the difference in means under the null hypothesis.
+*     -   a zero-dimensional ndarray specifying the known standard deviation of first one-dimensional input ndarray.
+*     -   a zero-dimensional ndarray specifying the known standard deviation of second one-dimensional input ndarray.
+*
+* @param arrays - array-like object containing ndarrays
+* @returns output ndarray
+*
+* @example
+* var Float64Results = require( '@stdlib/stats/base/ztest/two-sample/results/float64' );
+* var resolveEnum = require( '@stdlib/stats/base/ztest/alternative-resolve-enum' );
+* var structFactory = require( '@stdlib/array/struct-factory' );
+* var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+* var ndarray = require( '@stdlib/ndarray/ctor' );
+*
+* var opts = {
+*     'dtype': 'generic'
+* };
+*
+* // Define a one-dimensional input ndarray:
+* var xbuf = [ 4.0, 4.0, 6.0, 6.0, 5.0 ];
+* var x = new ndarray( opts.dtype, xbuf, [ 5 ], [ 1 ], 0, 'row-major' );
+*
+* var ybuf = [ 3.0, 3.0, 5.0, 7.0, 7.0 ];
+* var y = new ndarray( opts.dtype, ybuf, [ 5 ], [ 1 ], 0, 'row-major' );
+*
+* // Specify the alternative hypothesis:
+* var alt = scalar2ndarray( resolveEnum( 'two-sided' ), {
+*     'dtype': 'int8'
+* });
+*
+* // Specify the significance level:
+* var alpha = scalar2ndarray( 0.05, opts );
+*
+* // Specify the difference in means under the null hypothesis:
+* var diff = scalar2ndarray( 0.0, opts );
+*
+* // Specify the known standard deviations:
+* var sigmax = scalar2ndarray( 1.0, opts );
+* var sigmay = scalar2ndarray( 2.0, opts );
+*
+* // Create a zero-dimensional results ndarray:
+* var ResultsArray = structFactory( Float64Results );
+* var out = new ndarray( Float64Results, new ResultsArray( 1 ), [], [ 0 ], 0, 'row-major' );
+*
+* // Perform a Z-test:
+* var v = ztest2( [ x, y, out, alt, alpha, diff, sigmax, sigmay ] );
+* // returns <ResultsArray>
+*
+* console.log( v.get().toString() );
+*/
+declare function ztest2<T extends typedndarray<number>, U extends ndarray>( arrays: [ T, T, U, T, T, T, T, T ] ): U;
+
+
+// EXPORTS //
+
+export = ztest2;
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/docs/types/test.ts b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/docs/types/test.ts
new file mode 100644
index 000000000000..17725386d442
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/docs/types/test.ts
@@ -0,0 +1,57 @@
+/*
+* @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.
+*/
+
+/* eslint-disable space-in-parens */
+
+import zeros = require( '@stdlib/ndarray/zeros' );
+import ztest2 = require( './index' );
+
+
+// TESTS //
+
+// The function returns an ndarray...
+{
+	const x = zeros( [ 10 ], {
+		'dtype': 'float64'
+	});
+
+	ztest2( [ x, x, x, x, x, x, x, x ] ); // $ExpectType float64ndarray
+}
+
+// The compiler throws an error if the function is provided a first argument which is not an array of ndarrays...
+{
+	ztest2( '10' ); // $ExpectError
+	ztest2( 10 ); // $ExpectError
+	ztest2( true ); // $ExpectError
+	ztest2( false ); // $ExpectError
+	ztest2( null ); // $ExpectError
+	ztest2( undefined ); // $ExpectError
+	ztest2( [] ); // $ExpectError
+	ztest2( {} ); // $ExpectError
+	ztest2( ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided an unsupported number of arguments...
+{
+	const x = zeros( [ 10 ], {
+		'dtype': 'float64'
+	});
+
+	ztest2(); // $ExpectError
+	ztest2( [ x, x, x, x, x, x ], {} ); // $ExpectError
+}
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/examples/index.js b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/examples/index.js
new file mode 100644
index 000000000000..557f49da3f4c
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/examples/index.js
@@ -0,0 +1,64 @@
+/**
+* @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';
+
+var Float64Results = require( '@stdlib/stats/base/ztest/two-sample/results/float64' );
+var resolveEnum = require( '@stdlib/stats/base/ztest/alternative-resolve-enum' );
+var structFactory = require( '@stdlib/array/struct-factory' );
+var normal = require( '@stdlib/random/array/normal' );
+var ndarray = require( '@stdlib/ndarray/ctor' );
+var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+var ndarray2array = require( '@stdlib/ndarray/to-array' );
+var ztest2 = require( './../lib' );
+
+var opts = {
+	'dtype': 'generic'
+};
+
+// Create a one-dimensional ndarrays containing pseudorandom numbers drawn from a normal distribution:
+var xbuf = normal( 100, 0.0, 1.0, opts );
+var x = new ndarray( opts.dtype, xbuf, [ xbuf.length ], [ 1 ], 0, 'row-major' );
+console.log( ndarray2array( x ) );
+
+var ybuf = normal( 100, 0.0, 1.0, opts );
+var y = new ndarray( opts.dtype, ybuf, [ ybuf.length ], [ 1 ], 0, 'row-major' );
+console.log( ndarray2array( y ) );
+
+// Specify the alternative hypothesis:
+var alt = scalar2ndarray( resolveEnum( 'two-sided' ), {
+	'dtype': 'int8'
+});
+
+// Specify the significance level:
+var alpha = scalar2ndarray( 0.05, opts );
+
+// Specify the difference in means under the null hypothesis:
+var diff = scalar2ndarray( 0.0, opts );
+
+// Specify the known standard deviations:
+var sigmax = scalar2ndarray( 1.0, opts );
+var sigmay = scalar2ndarray( 1.0, opts );
+
+// Create a zero-dimensional results ndarray:
+var ResultsArray = structFactory( Float64Results );
+var out = new ndarray( Float64Results, new ResultsArray( 1 ), [], [ 0 ], 0, 'row-major' );
+
+// Perform a Z-test:
+var v = ztest2( [ x, y, out, alt, alpha, diff, sigmax, sigmay ] );
+console.log( v.get().toString() );
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/lib/index.js b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/lib/index.js
new file mode 100644
index 000000000000..27203c9b61cf
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/lib/index.js
@@ -0,0 +1,78 @@
+/**
+* @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';
+
+/**
+* Compute a two-sample Z-test for two one-dimensional ndarrays.
+*
+* @module @stdlib/stats/base/ndarray/ztest2
+*
+* @example
+* var Float64Results = require( '@stdlib/stats/base/ztest/two-sample/results/float64' );
+* var resolveEnum = require( '@stdlib/stats/base/ztest/alternative-resolve-enum' );
+* var structFactory = require( '@stdlib/array/struct-factory' );
+* var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+* var ndarray = require( '@stdlib/ndarray/ctor' );
+* var ztest2 = require( '@stdlib/stats/base/ndarray/ztest2' );
+*
+* var opts = {
+*     'dtype': 'generic'
+* };
+*
+* // Define a one-dimensional input ndarray:
+* var xbuf = [ 4.0, 4.0, 6.0, 6.0, 5.0 ];
+* var x = new ndarray( opts.dtype, xbuf, [ 5 ], [ 1 ], 0, 'row-major' );
+*
+* var ybuf = [ 3.0, 3.0, 5.0, 7.0, 7.0 ];
+* var y = new ndarray( opts.dtype, ybuf, [ 5 ], [ 1 ], 0, 'row-major' );
+*
+* // Specify the alternative hypothesis:
+* var alt = scalar2ndarray( resolveEnum( 'two-sided' ), {
+*     'dtype': 'int8'
+* });
+*
+* // Specify the significance level:
+* var alpha = scalar2ndarray( 0.05, opts );
+*
+* // Specify the difference in means under the null hypothesis:
+* var diff = scalar2ndarray( 0.0, opts );
+*
+* // Specify the known standard deviations:
+* var sigmax = scalar2ndarray( 1.0, opts );
+* var sigmay = scalar2ndarray( 2.0, opts );
+*
+* // Create a zero-dimensional results ndarray:
+* var ResultsArray = structFactory( Float64Results );
+* var out = new ndarray( Float64Results, new ResultsArray( 1 ), [], [ 0 ], 0, 'row-major' );
+*
+* // Perform a Z-test:
+* var v = ztest2( [ x, y, out, alt, alpha, diff, sigmax, sigmay ] );
+* // returns <ResultsArray>
+*
+* console.log( v.get().toString() );
+*/
+
+// MODULES //
+
+var main = require( './main.js' );
+
+
+// EXPORTS //
+
+module.exports = main;
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/lib/main.js b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/lib/main.js
new file mode 100644
index 000000000000..a64e113fc4b2
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/lib/main.js
@@ -0,0 +1,123 @@
+/**
+* @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 numelDimension = require( '@stdlib/ndarray/base/numel-dimension' );
+var getStride = require( '@stdlib/ndarray/base/stride' );
+var getOffset = require( '@stdlib/ndarray/base/offset' );
+var getData = require( '@stdlib/ndarray/base/data-buffer' );
+var ndarraylike2scalar = require( '@stdlib/ndarray/base/ndarraylike2scalar' );
+var strided = require( '@stdlib/stats/strided/ztest2' ).ndarray;
+
+
+// MAIN //
+
+/**
+* Computes a two-sample Z-test for two one-dimensional ndarrays.
+*
+* ## Notes
+*
+* -   The function expects the following ndarrays in order:
+*
+*     -   first one-dimensional input ndarray.
+*     -   second one-dimensional input ndarray.
+*     -   a zero-dimensional output ndarray containing a results object.
+*     -   a zero-dimensional ndarray specifying the alternative hypothesis.
+*     -   a zero-dimensional ndarray specifying the significance level.
+*     -   a zero-dimensional ndarray specifying the difference in means under the null hypothesis.
+*     -   a zero-dimensional ndarray specifying the known standard deviation of first one-dimensional input ndarray.
+*     -   a zero-dimensional ndarray specifying the known standard deviation of second one-dimensional input ndarray.
+*
+* @param {ArrayLikeObject<Object>} arrays - array-like object containing ndarrays
+* @returns {ndarrayLike} output ndarray
+*
+* @example
+* var Float64Results = require( '@stdlib/stats/base/ztest/two-sample/results/float64' );
+* var resolveEnum = require( '@stdlib/stats/base/ztest/alternative-resolve-enum' );
+* var structFactory = require( '@stdlib/array/struct-factory' );
+* var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+* var ndarray = require( '@stdlib/ndarray/ctor' );
+*
+* var opts = {
+*     'dtype': 'generic'
+* };
+*
+* // Define a one-dimensional input ndarray:
+* var xbuf = [ 4.0, 4.0, 6.0, 6.0, 5.0 ];
+* var x = new ndarray( opts.dtype, xbuf, [ 5 ], [ 1 ], 0, 'row-major' );
+*
+* var ybuf = [ 3.0, 3.0, 5.0, 7.0, 7.0 ];
+* var y = new ndarray( opts.dtype, ybuf, [ 5 ], [ 1 ], 0, 'row-major' );
+*
+* // Specify the alternative hypothesis:
+* var alt = scalar2ndarray( resolveEnum( 'two-sided' ), {
+*     'dtype': 'int8'
+* });
+*
+* // Specify the significance level:
+* var alpha = scalar2ndarray( 0.05, opts );
+*
+* // Specify the difference in means under the null hypothesis:
+* var diff = scalar2ndarray( 0.0, opts );
+*
+* // Specify the known standard deviations:
+* var sigmax = scalar2ndarray( 1.0, opts );
+* var sigmay = scalar2ndarray( 2.0, opts );
+*
+* // Create a zero-dimensional results ndarray:
+* var ResultsArray = structFactory( Float64Results );
+* var out = new ndarray( Float64Results, new ResultsArray( 1 ), [], [ 0 ], 0, 'row-major' );
+*
+* // Perform a Z-test:
+* var v = ztest2( [ x, y, out, alt, alpha, diff, sigmax, sigmay ] );
+* // returns <ResultsArray>
+*
+* console.log( v.get().toString() );
+*/
+function ztest2( arrays ) {
+	var sigmax;
+	var sigmay;
+	var alpha;
+	var diff;
+	var alt;
+	var out;
+	var x;
+	var y;
+
+	x = arrays[ 0 ];
+	y = arrays[ 1 ];
+	out = ndarraylike2scalar( arrays[ 2 ] );
+
+	alt = ndarraylike2scalar( arrays[ 3 ] );
+	alpha = ndarraylike2scalar( arrays[ 4 ] );
+	diff = ndarraylike2scalar( arrays[ 5 ] );
+	sigmax = ndarraylike2scalar( arrays[ 6 ] );
+	sigmay = ndarraylike2scalar( arrays[ 7 ] );
+
+	strided( numelDimension( x, 0 ), numelDimension( y, 0 ), alt, alpha, diff, sigmax, getData( x ), getStride( x, 0 ), getOffset( x ), sigmay, getData( y ), getStride( y, 0 ), getOffset( y ), out ); // eslint-disable-line max-len
+
+	return arrays[ 2 ];
+}
+
+
+// EXPORTS //
+
+module.exports = ztest2;
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/package.json b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/package.json
new file mode 100644
index 000000000000..b3694c78993c
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/package.json
@@ -0,0 +1,65 @@
+{
+  "name": "@stdlib/stats/base/ndarray/ztest2",
+  "version": "0.0.0",
+  "description": "Compute a two-sample Z-test for two one-dimensional ndarrays.",
+  "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",
+    "z-test",
+    "ztest",
+    "hypothesis",
+    "normality",
+    "ndarray"
+  ],
+  "__stdlib__": {}
+}
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/test/test.js b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/test/test.js
new file mode 100644
index 000000000000..fc4081308233
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/test/test.js
@@ -0,0 +1,352 @@
+/**
+* @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.
+*/
+
+/* eslint-disable max-len */
+
+'use strict';
+
+// MODULES //
+
+var tape = require( 'tape' );
+var Float64Results = require( '@stdlib/stats/base/ztest/two-sample/results/float64' );
+var resolveEnum = require( '@stdlib/stats/base/ztest/alternative-resolve-enum' );
+var structFactory = require( '@stdlib/array/struct-factory' );
+var normal = require( '@stdlib/random/strided/normal' ).ndarray;
+var zeros = require( '@stdlib/array/zeros' );
+var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+var ndarray = require( '@stdlib/ndarray/base/ctor' );
+var ztest2 = require( './../lib' );
+
+
+// VARIABLES //
+
+var ResultsArray = structFactory( Float64Results );
+var RANDOM_OPTS = {
+	'seed': 12345
+};
+
+
+// FUNCTIONS //
+
+/**
+* Returns a one-dimensional ndarray.
+*
+* @private
+* @param {Collection} buffer - underlying data buffer
+* @param {NonNegativeInteger} length - number of indexed elements
+* @param {integer} stride - stride length
+* @param {NonNegativeInteger} offset - index offset
+* @returns {ndarray} one-dimensional ndarray
+*/
+function vector( buffer, length, stride, offset ) {
+	return new ndarray( 'generic', buffer, [ length ], [ stride ], offset, 'row-major' );
+}
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+	t.ok( true, __filename );
+	t.strictEqual( typeof ztest2, 'function', 'main export is a function' );
+	t.end();
+});
+
+tape( 'the function has an arity of 1', function test( t ) {
+	t.strictEqual( ztest2.length, 1, 'has expected arity' );
+	t.end();
+});
+
+tape( 'the function performs a Z-test over two one-dimensional ndarrays (two-sided)', function test( t ) {
+	var sigmax;
+	var sigmay;
+	var alpha;
+	var diff;
+	var opts;
+	var xbuf;
+	var ybuf;
+	var obuf;
+	var alt;
+	var out;
+	var x;
+	var y;
+	var v;
+
+	opts = {
+		'dtype': 'generic'
+	};
+
+	alt = scalar2ndarray( resolveEnum( 'two-sided' ), {
+		'dtype': 'int8'
+	});
+	alpha = scalar2ndarray( 0.1, opts );
+	sigmax = scalar2ndarray( 1.0, opts );
+	sigmay = scalar2ndarray( 1.0, opts );
+
+	obuf = new ResultsArray( 1 );
+	out = new ndarray( Float64Results, obuf, [], [ 0 ], 0, 'row-major' );
+
+	// Generate a large enough arrays to effectively guarantee results...
+	xbuf = zeros( 10000, opts.dtype );
+	ybuf = zeros( 10000, opts.dtype );
+
+	normal( xbuf.length, [ 0.0 ], 0, 0, [ 1.0 ], 0, 0, xbuf, 1, 0, RANDOM_OPTS );
+	x = vector( xbuf, xbuf.length, 1, 0 );
+
+	normal( ybuf.length, [ 0.0 ], 0, 0, [ 1.0 ], 0, 0, ybuf, 1, 0, RANDOM_OPTS );
+	y = vector( ybuf, ybuf.length, 1, 0 );
+
+	diff = scalar2ndarray( 0.0, opts );
+	v = ztest2( [ x, y, out, alt, alpha, diff, sigmax, sigmay ] );
+	t.strictEqual( v, out, 'returns expected value' );
+	t.strictEqual( out.get().rejected, false, 'returns expected value' );
+
+	diff = scalar2ndarray( 10.0, opts );
+	v = ztest2( [ x, y, out, alt, alpha, diff, sigmax, sigmay ] );
+	t.strictEqual( v, out, 'returns expected value' );
+	t.strictEqual( out.get().rejected, true, 'returns expected value' );
+
+	normal( xbuf.length, [ 4.0 ], 0, 0, [ 1.0 ], 0, 0, xbuf, 1, 0, RANDOM_OPTS );
+	normal( ybuf.length, [ 2.0 ], 0, 0, [ 1.0 ], 0, 0, ybuf, 1, 0, RANDOM_OPTS );
+
+	diff = scalar2ndarray( 1.0, opts );
+	v = ztest2( [ x, y, out, alt, alpha, diff, sigmax, sigmay ] );
+	t.strictEqual( v, out, 'returns expected value' );
+	t.strictEqual( out.get().rejected, true, 'returns expected value' );
+
+	t.end();
+});
+
+tape( 'the function performs a Z-test over two one-dimensional ndarrays (less)', function test( t ) {
+	var sigmax;
+	var sigmay;
+	var alpha;
+	var diff;
+	var opts;
+	var xbuf;
+	var ybuf;
+	var obuf;
+	var alt;
+	var out;
+	var x;
+	var y;
+	var v;
+
+	opts = {
+		'dtype': 'generic'
+	};
+
+	alt = scalar2ndarray( resolveEnum( 'less' ), {
+		'dtype': 'int8'
+	});
+	alpha = scalar2ndarray( 0.1, opts );
+	sigmax = scalar2ndarray( 1.0, opts );
+	sigmay = scalar2ndarray( 1.0, opts );
+
+	obuf = new ResultsArray( 1 );
+	out = new ndarray( Float64Results, obuf, [], [ 0 ], 0, 'row-major' );
+
+	// Generate a large enough arrays to effectively guarantee results...
+	xbuf = zeros( 10000, opts.dtype );
+	ybuf = zeros( 10000, opts.dtype );
+
+	normal( xbuf.length, [ 2.0 ], 0, 0, [ 1.0 ], 0, 0, xbuf, 1, 0, RANDOM_OPTS );
+	x = vector( xbuf, xbuf.length, 1, 0 );
+
+	normal( ybuf.length, [ 0.0 ], 0, 0, [ 1.0 ], 0, 0, ybuf, 1, 0, RANDOM_OPTS );
+	y = vector( ybuf, ybuf.length, 1, 0 );
+
+	diff = scalar2ndarray( 0.0, opts );
+	v = ztest2( [ x, y, out, alt, alpha, diff, sigmax, sigmay ] );
+	t.strictEqual( v, out, 'returns expected value' );
+	t.strictEqual( out.get().rejected, false, 'returns expected value' );
+
+	normal( xbuf.length, [ 0.0 ], 0, 0, [ 1.0 ], 0, 0, xbuf, 1, 0, RANDOM_OPTS );
+	normal( ybuf.length, [ 0.0 ], 0, 0, [ 1.0 ], 0, 0, ybuf, 1, 0, RANDOM_OPTS );
+
+	diff = scalar2ndarray( 1.0, opts );
+	v = ztest2( [ x, y, out, alt, alpha, diff, sigmax, sigmay ] );
+	t.strictEqual( v, out, 'returns expected value' );
+	t.strictEqual( out.get().rejected, true, 'returns expected value' );
+
+	t.end();
+});
+
+tape( 'the function performs a Z-test over two one-dimensional ndarrays (greater)', function test( t ) {
+	var sigmax;
+	var sigmay;
+	var alpha;
+	var diff;
+	var opts;
+	var xbuf;
+	var ybuf;
+	var obuf;
+	var alt;
+	var out;
+	var x;
+	var y;
+	var v;
+
+	opts = {
+		'dtype': 'generic'
+	};
+
+	alt = scalar2ndarray( resolveEnum( 'greater' ), {
+		'dtype': 'int8'
+	});
+	alpha = scalar2ndarray( 0.1, opts );
+	sigmax = scalar2ndarray( 1.0, opts );
+	sigmay = scalar2ndarray( 1.0, opts );
+
+	obuf = new ResultsArray( 1 );
+	out = new ndarray( Float64Results, obuf, [], [ 0 ], 0, 'row-major' );
+
+	// Generate a large enough arrays to effectively guarantee results...
+	xbuf = zeros( 10000, opts.dtype );
+	ybuf = zeros( 10000, opts.dtype );
+
+	normal( xbuf.length, [ 0.0 ], 0, 0, [ 1.0 ], 0, 0, xbuf, 1, 0, RANDOM_OPTS );
+	x = vector( xbuf, xbuf.length, 1, 0 );
+
+	normal( ybuf.length, [ 2.0 ], 0, 0, [ 1.0 ], 0, 0, ybuf, 1, 0, RANDOM_OPTS );
+	y = vector( ybuf, ybuf.length, 1, 0 );
+
+	diff = scalar2ndarray( 0.0, opts );
+	v = ztest2( [ x, y, out, alt, alpha, diff, sigmax, sigmay ] );
+	t.strictEqual( v, out, 'returns expected value' );
+	t.strictEqual( out.get().rejected, false, 'returns expected value' );
+
+	normal( xbuf.length, [ 0.0 ], 0, 0, [ 1.0 ], 0, 0, xbuf, 1, 0, RANDOM_OPTS );
+	normal( ybuf.length, [ 0.0 ], 0, 0, [ 1.0 ], 0, 0, ybuf, 1, 0, RANDOM_OPTS );
+
+	diff = scalar2ndarray( -1.0, opts );
+	v = ztest2( [ x, y, out, alt, alpha, diff, sigmax, sigmay ] );
+	t.strictEqual( v, out, 'returns expected value' );
+	t.strictEqual( out.get().rejected, true, 'returns expected value' );
+
+	t.end();
+});
+
+tape( 'the function supports one-dimensional ndarrays having non-unit strides', function test( t ) {
+	var sigmax;
+	var sigmay;
+	var alpha;
+	var diff;
+	var opts;
+	var xbuf;
+	var ybuf;
+	var obuf;
+	var alt;
+	var out;
+	var x;
+	var y;
+	var v;
+
+	opts = {
+		'dtype': 'generic'
+	};
+
+	alt = scalar2ndarray( resolveEnum( 'two-sided' ), {
+		'dtype': 'int8'
+	});
+	alpha = scalar2ndarray( 0.1, opts );
+	sigmax = scalar2ndarray( 1.0, opts );
+	sigmay = scalar2ndarray( 1.0, opts );
+
+	obuf = new ResultsArray( 1 );
+	out = new ndarray( Float64Results, obuf, [], [ 0 ], 0, 'row-major' );
+
+	// Generate a large enough arrays to effectively guarantee results...
+	xbuf = zeros( 10000, opts.dtype );
+	ybuf = zeros( 10000, opts.dtype );
+
+	normal( 5000, [ 0.0 ], 0, 0, [ 1.0 ], 0, 0, xbuf, 2, 0, RANDOM_OPTS );
+	x = vector( xbuf, 5000, 2, 0 );
+
+	normal( 5000, [ 0.0 ], 0, 0, [ 1.0 ], 0, 0, ybuf, 2, 0, RANDOM_OPTS );
+	y = vector( ybuf, 5000, 2, 0 );
+
+	diff = scalar2ndarray( 0.0, opts );
+	v = ztest2( [ x, y, out, alt, alpha, diff, sigmax, sigmay ] );
+	t.strictEqual( v, out, 'returns expected value' );
+	t.strictEqual( out.get().rejected, false, 'returns expected value' );
+
+	normal( 5000, [ 4.0 ], 0, 0, [ 1.0 ], 0, 0, xbuf, 2, 0, RANDOM_OPTS );
+	normal( 5000, [ 2.0 ], 0, 0, [ 1.0 ], 0, 0, ybuf, 2, 0, RANDOM_OPTS );
+
+	diff = scalar2ndarray( 10.0, opts );
+	v = ztest2( [ x, y, out, alt, alpha, diff, sigmax, sigmay ] );
+	t.strictEqual( v, out, 'returns expected value' );
+	t.strictEqual( out.get().rejected, true, 'returns expected value' );
+
+	t.end();
+});
+
+tape( 'the function supports one-dimensional ndarrays having non-zero offsets', function test( t ) {
+	var sigmax;
+	var sigmay;
+	var alpha;
+	var diff;
+	var opts;
+	var xbuf;
+	var ybuf;
+	var obuf;
+	var alt;
+	var out;
+	var x;
+	var y;
+	var v;
+
+	opts = {
+		'dtype': 'generic'
+	};
+
+	alt = scalar2ndarray( resolveEnum( 'two-sided' ), {
+		'dtype': 'int8'
+	});
+	alpha = scalar2ndarray( 0.1, opts );
+	sigmax = scalar2ndarray( 1.0, opts );
+	sigmay = scalar2ndarray( 1.0, opts );
+
+	obuf = new ResultsArray( 1 );
+	out = new ndarray( Float64Results, obuf, [], [ 0 ], 0, 'row-major' );
+
+	// Generate a large enough arrays to effectively guarantee results...
+	xbuf = zeros( 10000, opts.dtype );
+	ybuf = zeros( 10000, opts.dtype );
+
+	normal( 5000, [ 0.0 ], 0, 0, [ 1.0 ], 0, 0, xbuf, 1, 5000, RANDOM_OPTS );
+	x = vector( xbuf, 5000, 1, 5000 );
+
+	normal( 5000, [ 0.0 ], 0, 0, [ 1.0 ], 0, 0, ybuf, 1, 5000, RANDOM_OPTS );
+	y = vector( ybuf, 5000, 1, 5000 );
+
+	diff = scalar2ndarray( 0.0, opts );
+	v = ztest2( [ x, y, out, alt, alpha, diff, sigmax, sigmay ] );
+	t.strictEqual( v, out, 'returns expected value' );
+	t.strictEqual( out.get().rejected, false, 'returns expected value' );
+
+	normal( 5000, [ 100.0 ], 0, 0, [ 1.0 ], 0, 0, xbuf, 1, 5000, RANDOM_OPTS );
+	normal( 5000, [ 100.0 ], 0, 0, [ 1.0 ], 0, 0, ybuf, 1, 5000, RANDOM_OPTS );
+
+	diff = scalar2ndarray( 1.0, opts );
+	v = ztest2( [ x, y, out, alt, alpha, diff, sigmax, sigmay ] );
+	t.strictEqual( v, out, 'returns expected value' );
+	t.strictEqual( out.get().rejected, true, 'returns expected value' );
+
+	t.end();
+});

From 6166485f523781ea25fa6fe5bd4fb28c66449b57 Mon Sep 17 00:00:00 2001
From: gururaj1512 <gururajgurram1512@gmail.com>
Date: Sun, 20 Jul 2025 08:52:42 +0000
Subject: [PATCH 2/3] chore: fix comments

---
 lib/node_modules/@stdlib/stats/base/ndarray/ztest2/README.md    | 2 +-
 .../@stdlib/stats/base/ndarray/ztest2/docs/repl.txt             | 2 +-
 .../@stdlib/stats/base/ndarray/ztest2/docs/types/index.d.ts     | 2 +-
 .../@stdlib/stats/base/ndarray/ztest2/examples/index.js         | 2 +-
 lib/node_modules/@stdlib/stats/base/ndarray/ztest2/lib/index.js | 2 +-
 lib/node_modules/@stdlib/stats/base/ndarray/ztest2/lib/main.js  | 2 +-
 6 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/README.md b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/README.md
index 69ee6d503b8b..c80617273562 100644
--- a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/README.md
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/README.md
@@ -129,7 +129,7 @@ var opts = {
     'dtype': 'generic'
 };
 
-// Create a one-dimensional ndarrays containing pseudorandom numbers drawn from a normal distribution:
+// Create one-dimensional ndarrays containing pseudorandom numbers drawn from a normal distribution:
 var xbuf = normal( 100, 0.0, 1.0, opts );
 var x = new ndarray( opts.dtype, xbuf, [ xbuf.length ], [ 1 ], 0, 'row-major' );
 console.log( ndarray2array( x ) );
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/docs/repl.txt b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/docs/repl.txt
index 13050aad8a6b..f263aa204bc8 100644
--- a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/docs/repl.txt
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/docs/repl.txt
@@ -26,7 +26,7 @@
 
     Examples
     --------
-    // Create the input ndarray:
+    // Create input ndarrays:
     > var xbuf = [ 4.0, 4.0, 6.0, 6.0, 5.0 ];
     > var ybuf = [ 3.0, 3.0, 5.0, 7.0, 7.0 ];
     > var dt = 'generic';
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/docs/types/index.d.ts b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/docs/types/index.d.ts
index 2563ce3caf5c..2d78f8a7a5a9 100644
--- a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/docs/types/index.d.ts
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/docs/types/index.d.ts
@@ -52,7 +52,7 @@ import { typedndarray, ndarray } from '@stdlib/types/ndarray';
 *     'dtype': 'generic'
 * };
 *
-* // Define a one-dimensional input ndarray:
+* // Define one-dimensional input ndarrays:
 * var xbuf = [ 4.0, 4.0, 6.0, 6.0, 5.0 ];
 * var x = new ndarray( opts.dtype, xbuf, [ 5 ], [ 1 ], 0, 'row-major' );
 *
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/examples/index.js b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/examples/index.js
index 557f49da3f4c..f1cbb9b7d7f2 100644
--- a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/examples/index.js
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/examples/index.js
@@ -31,7 +31,7 @@ var opts = {
 	'dtype': 'generic'
 };
 
-// Create a one-dimensional ndarrays containing pseudorandom numbers drawn from a normal distribution:
+// Create one-dimensional ndarrays containing pseudorandom numbers drawn from a normal distribution:
 var xbuf = normal( 100, 0.0, 1.0, opts );
 var x = new ndarray( opts.dtype, xbuf, [ xbuf.length ], [ 1 ], 0, 'row-major' );
 console.log( ndarray2array( x ) );
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/lib/index.js b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/lib/index.js
index 27203c9b61cf..d4b46840d00e 100644
--- a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/lib/index.js
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/lib/index.js
@@ -35,7 +35,7 @@
 *     'dtype': 'generic'
 * };
 *
-* // Define a one-dimensional input ndarray:
+* // Define one-dimensional input ndarrays:
 * var xbuf = [ 4.0, 4.0, 6.0, 6.0, 5.0 ];
 * var x = new ndarray( opts.dtype, xbuf, [ 5 ], [ 1 ], 0, 'row-major' );
 *
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/lib/main.js b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/lib/main.js
index a64e113fc4b2..7a51dc41320e 100644
--- a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/lib/main.js
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/lib/main.js
@@ -60,7 +60,7 @@ var strided = require( '@stdlib/stats/strided/ztest2' ).ndarray;
 *     'dtype': 'generic'
 * };
 *
-* // Define a one-dimensional input ndarray:
+* // Define one-dimensional input ndarrays:
 * var xbuf = [ 4.0, 4.0, 6.0, 6.0, 5.0 ];
 * var x = new ndarray( opts.dtype, xbuf, [ 5 ], [ 1 ], 0, 'row-major' );
 *

From 1a2d1b703d5dfb58bf5c5838be6e728b1c52e58d Mon Sep 17 00:00:00 2001
From: gururaj1512 <gururajgurram1512@gmail.com>
Date: Mon, 21 Jul 2025 07:08:53 +0000
Subject: [PATCH 3/3] chore: clean-up

---
 .../@stdlib/stats/base/ndarray/ztest2/README.md    | 14 +++++++-------
 .../stats/base/ndarray/ztest2/docs/repl.txt        |  4 ++--
 .../base/ndarray/ztest2/docs/types/index.d.ts      |  4 ++--
 .../@stdlib/stats/base/ndarray/ztest2/lib/main.js  |  4 ++--
 .../@stdlib/stats/base/ndarray/ztest2/test/test.js | 10 +++++-----
 5 files changed, 18 insertions(+), 18 deletions(-)

diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/README.md b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/README.md
index c80617273562..a5c9504809cc 100644
--- a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/README.md
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/README.md
@@ -87,13 +87,13 @@ The function has the following parameters:
 -   **arrays**: array-like object containing the following ndarrays in order:
 
     1.  first one-dimensional input ndarray.
-    1.  second one-dimensional input ndarray.
-    2.  a zero-dimensional output ndarray containing a [results object][@stdlib/stats/base/ztest/two-sample/results/float64].
-    3.  a zero-dimensional ndarray specifying the alternative hypothesis.
-    4.  a zero-dimensional ndarray specifying the significance level.
-    5.  a zero-dimensional ndarray specifying the difference in means under the null hypothesis.
-    6.  a zero-dimensional ndarray specifying the known standard deviation of first one-dimensional input ndarray.
-    7.  a zero-dimensional ndarray specifying the known standard deviation of second one-dimensional input ndarray.
+    2.  second one-dimensional input ndarray.
+    3.  a zero-dimensional output ndarray containing a [results object][@stdlib/stats/base/ztest/two-sample/results/float64].
+    4.  a zero-dimensional ndarray specifying the alternative hypothesis.
+    5.  a zero-dimensional ndarray specifying the significance level.
+    6.  a zero-dimensional ndarray specifying the difference in means under the null hypothesis.
+    7.  a zero-dimensional ndarray specifying the known standard deviation of the first one-dimensional input ndarray.
+    8.  a zero-dimensional ndarray specifying the known standard deviation of the second one-dimensional input ndarray.
 
 </section>
 
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/docs/repl.txt b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/docs/repl.txt
index f263aa204bc8..de38f914846c 100644
--- a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/docs/repl.txt
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/docs/repl.txt
@@ -15,9 +15,9 @@
         - a zero-dimensional ndarray specifying the difference in means under
         the null hypothesis.
         - a zero-dimensional ndarray specifying the known standard deviation of
-        first one-dimensional input ndarray.
+        the first one-dimensional input ndarray.
         - a zero-dimensional ndarray specifying the known standard deviation of
-        second one-dimensional input ndarray.
+        the second one-dimensional input ndarray.
 
     Returns
     -------
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/docs/types/index.d.ts b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/docs/types/index.d.ts
index 2d78f8a7a5a9..b10d6cfef2f5 100644
--- a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/docs/types/index.d.ts
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/docs/types/index.d.ts
@@ -35,8 +35,8 @@ import { typedndarray, ndarray } from '@stdlib/types/ndarray';
 *     -   a zero-dimensional ndarray specifying the alternative hypothesis.
 *     -   a zero-dimensional ndarray specifying the significance level.
 *     -   a zero-dimensional ndarray specifying the difference in means under the null hypothesis.
-*     -   a zero-dimensional ndarray specifying the known standard deviation of first one-dimensional input ndarray.
-*     -   a zero-dimensional ndarray specifying the known standard deviation of second one-dimensional input ndarray.
+*     -   a zero-dimensional ndarray specifying the known standard deviation of the first one-dimensional input ndarray.
+*     -   a zero-dimensional ndarray specifying the known standard deviation of the second one-dimensional input ndarray.
 *
 * @param arrays - array-like object containing ndarrays
 * @returns output ndarray
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/lib/main.js b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/lib/main.js
index 7a51dc41320e..94961ca6b6fd 100644
--- a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/lib/main.js
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/lib/main.js
@@ -43,8 +43,8 @@ var strided = require( '@stdlib/stats/strided/ztest2' ).ndarray;
 *     -   a zero-dimensional ndarray specifying the alternative hypothesis.
 *     -   a zero-dimensional ndarray specifying the significance level.
 *     -   a zero-dimensional ndarray specifying the difference in means under the null hypothesis.
-*     -   a zero-dimensional ndarray specifying the known standard deviation of first one-dimensional input ndarray.
-*     -   a zero-dimensional ndarray specifying the known standard deviation of second one-dimensional input ndarray.
+*     -   a zero-dimensional ndarray specifying the known standard deviation of the first one-dimensional input ndarray.
+*     -   a zero-dimensional ndarray specifying the known standard deviation of the second one-dimensional input ndarray.
 *
 * @param {ArrayLikeObject<Object>} arrays - array-like object containing ndarrays
 * @returns {ndarrayLike} output ndarray
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/test/test.js b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/test/test.js
index fc4081308233..426b7e8b11c4 100644
--- a/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/test/test.js
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/ztest2/test/test.js
@@ -100,7 +100,7 @@ tape( 'the function performs a Z-test over two one-dimensional ndarrays (two-sid
 	obuf = new ResultsArray( 1 );
 	out = new ndarray( Float64Results, obuf, [], [ 0 ], 0, 'row-major' );
 
-	// Generate a large enough arrays to effectively guarantee results...
+	// Generate large enough arrays to effectively guarantee results...
 	xbuf = zeros( 10000, opts.dtype );
 	ybuf = zeros( 10000, opts.dtype );
 
@@ -160,7 +160,7 @@ tape( 'the function performs a Z-test over two one-dimensional ndarrays (less)',
 	obuf = new ResultsArray( 1 );
 	out = new ndarray( Float64Results, obuf, [], [ 0 ], 0, 'row-major' );
 
-	// Generate a large enough arrays to effectively guarantee results...
+	// Generate large enough arrays to effectively guarantee results...
 	xbuf = zeros( 10000, opts.dtype );
 	ybuf = zeros( 10000, opts.dtype );
 
@@ -215,7 +215,7 @@ tape( 'the function performs a Z-test over two one-dimensional ndarrays (greater
 	obuf = new ResultsArray( 1 );
 	out = new ndarray( Float64Results, obuf, [], [ 0 ], 0, 'row-major' );
 
-	// Generate a large enough arrays to effectively guarantee results...
+	// Generate large enough arrays to effectively guarantee results...
 	xbuf = zeros( 10000, opts.dtype );
 	ybuf = zeros( 10000, opts.dtype );
 
@@ -270,7 +270,7 @@ tape( 'the function supports one-dimensional ndarrays having non-unit strides',
 	obuf = new ResultsArray( 1 );
 	out = new ndarray( Float64Results, obuf, [], [ 0 ], 0, 'row-major' );
 
-	// Generate a large enough arrays to effectively guarantee results...
+	// Generate large enough arrays to effectively guarantee results...
 	xbuf = zeros( 10000, opts.dtype );
 	ybuf = zeros( 10000, opts.dtype );
 
@@ -325,7 +325,7 @@ tape( 'the function supports one-dimensional ndarrays having non-zero offsets',
 	obuf = new ResultsArray( 1 );
 	out = new ndarray( Float64Results, obuf, [], [ 0 ], 0, 'row-major' );
 
-	// Generate a large enough arrays to effectively guarantee results...
+	// Generate large enough arrays to effectively guarantee results...
 	xbuf = zeros( 10000, opts.dtype );
 	ybuf = zeros( 10000, opts.dtype );