diff --git a/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/README.md b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/README.md
new file mode 100644
index 000000000000..f5bbc02c1ed7
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/README.md
@@ -0,0 +1,257 @@
+
+
+# Variance
+
+> [Log-logistic][log-logistic-distribution] distribution [variance][variance].
+
+
+
+The [variance][variance] for a [log-logistic][log-logistic-distribution] random variable with scale `α > 0` and shape `β > 2` is
+
+
+
+```math
+\operatorname{Var}\left[ X \right] = \alpha^2 \left( \frac{2b}{\sin 2b} - \frac{b^2}{\sin^2 b} \right), \quad b = \frac{\pi}{\beta}
+```
+
+
+
+where `b = π/β`.
+
+
+
+
+
+
+
+
+
+## Usage
+
+```javascript
+var variance = require( '@stdlib/stats/base/dists/log-logistic/variance' );
+```
+
+#### variance( alpha, beta )
+
+Returns the [variance][variance] of a [log-logistic][log-logistic-distribution] distribution with scale parameter `alpha` and shape parameter `beta`.
+
+```javascript
+var y = variance( 1.0, 3.0 );
+// returns ~0.956
+
+y = variance( 4.0, 3.0 );
+// returns ~15.300
+
+y = variance( 2.0, 5.0 );
+// returns ~0.715
+```
+
+If provided `NaN` as any argument, the function returns `NaN`.
+
+```javascript
+var y = variance( NaN, 3.0 );
+// returns NaN
+
+y = variance( 1.0, NaN );
+// returns NaN
+```
+
+If provided `alpha <= 0`, the function returns `NaN`.
+
+```javascript
+var y = variance( 0.0, 3.0 );
+// returns NaN
+
+y = variance( -1.0, 3.0 );
+// returns NaN
+```
+
+If provided `beta <= 2`, the function returns `NaN`.
+
+```javascript
+var y = variance( 2.0, 2.0 );
+// returns NaN
+
+y = variance( 2.0, 1.5 );
+// returns NaN
+```
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+## Examples
+
+
+
+```javascript
+var uniform = require( '@stdlib/random/array/uniform' );
+var logEachMap = require( '@stdlib/console/log-each-map' );
+var variance = require( '@stdlib/stats/base/dists/log-logistic/variance' );
+
+var opts = {
+ 'dtype': 'float64'
+};
+var alpha = uniform( 10, 0.1, 10.0, opts );
+var beta = uniform( 10, 2.1, 10.0, opts );
+
+logEachMap( 'α: %0.4f, β: %0.4f, Var(X;α,β): %0.4f', alpha, beta, variance );
+```
+
+
+
+
+
+
+
+* * *
+
+
+
+## C APIs
+
+
+
+
+
+
+
+
+
+
+
+### Usage
+
+```c
+#include "stdlib/stats/base/dists/log-logistic/variance.h"
+```
+
+#### stdlib_base_dists_log_logistic_variance( alpha, beta )
+
+Returns the variance of a log-logistic distribution with scale parameter `alpha` and shape parameter `beta`.
+
+```c
+double out = stdlib_base_dists_log_logistic_variance( 1.0, 3.0 );
+// returns ~0.956
+```
+
+The function accepts the following arguments:
+
+- **alpha**: `[in] double` scale parameter.
+- **beta**: `[in] double` shape parameter.
+
+```c
+double stdlib_base_dists_log_logistic_variance( const double alpha, const double beta );
+```
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+### Examples
+
+```c
+#include "stdlib/stats/base/dists/log-logistic/variance.h"
+#include
+#include
+
+static double random_uniform( const double min, const double max ) {
+ double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
+ return min + ( v*(max-min) );
+}
+
+int main( void ) {
+ double alpha;
+ double beta;
+ double v;
+ int i;
+
+ for ( i = 0; i < 25; i++ ) {
+ alpha = random_uniform( 0.1, 10.0 );
+ beta = random_uniform( 2.1, 10.0 );
+ v = stdlib_base_dists_log_logistic_variance( alpha, beta );
+ printf( "α: %lf, β: %lf, Var(X;α,β): %lf\n", alpha, beta, v );
+ }
+}
+```
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+[log-logistic-distribution]: https://en.wikipedia.org/wiki/Log-logistic_distribution
+
+[variance]: https://en.wikipedia.org/wiki/Variance
+
+
+
+
diff --git a/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/benchmark/benchmark.js b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/benchmark/benchmark.js
new file mode 100644
index 000000000000..7187ae9e6971
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/benchmark/benchmark.js
@@ -0,0 +1,59 @@
+/**
+* @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 uniform = require( '@stdlib/random/array/uniform' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+var pkg = require( './../package.json' ).name;
+var variance = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+ var alpha;
+ var beta;
+ var opts;
+ var y;
+ var i;
+
+ opts = {
+ 'dtype': 'float64'
+ };
+ alpha = uniform( 100, EPS, 10.0, opts );
+ beta = uniform( 100, 2.1, 10.0, opts );
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ y = variance( alpha[ i % alpha.length ], beta[ i % beta.length ] );
+ if ( isnan( y ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ }
+ b.toc();
+ if ( isnan( y ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ b.pass( 'benchmark finished' );
+ b.end();
+});
diff --git a/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/benchmark/benchmark.native.js b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/benchmark/benchmark.native.js
new file mode 100644
index 000000000000..a31ec1a84098
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/benchmark/benchmark.native.js
@@ -0,0 +1,69 @@
+/**
+* @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 resolve = require( 'path' ).resolve;
+var bench = require( '@stdlib/bench' );
+var tryRequire = require( '@stdlib/utils/try-require' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+var format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+
+
+// VARIABLES //
+
+var variance = tryRequire( resolve( __dirname, './../lib/native.js' ) );
+var opts = {
+ 'skip': ( variance instanceof Error )
+};
+
+
+// MAIN //
+
+bench( format( '%s::native', pkg ), opts, function benchmark( b ) {
+ var arrayOpts;
+ var alpha;
+ var beta;
+ var y;
+ var i;
+
+ arrayOpts = {
+ 'dtype': 'float64'
+ };
+ alpha = uniform( 100, EPS, 10.0, arrayOpts );
+ beta = uniform( 100, 2.1, 10.0, arrayOpts );
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ y = variance( alpha[ i % alpha.length ], beta[ i % beta.length ] );
+ if ( isnan( y ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ }
+ b.toc();
+ if ( isnan( y ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ b.pass( 'benchmark finished' );
+ b.end();
+});
diff --git a/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/benchmark/c/Makefile b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/benchmark/c/Makefile
new file mode 100644
index 000000000000..979768abbcec
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/benchmark/c/Makefile
@@ -0,0 +1,146 @@
+#/
+# @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.
+#/
+
+# VARIABLES #
+
+ifndef VERBOSE
+ QUIET := @
+else
+ QUIET :=
+endif
+
+# Determine the OS ([1][1], [2][2]).
+#
+# [1]: https://en.wikipedia.org/wiki/Uname#Examples
+# [2]: http://stackoverflow.com/a/27776822/2225624
+OS ?= $(shell uname)
+ifneq (, $(findstring MINGW,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring MSYS,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring CYGWIN,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring Windows_NT,$(OS)))
+ OS := WINNT
+endif
+endif
+endif
+endif
+
+# Define the program used for compiling C source files:
+ifdef C_COMPILER
+ CC := $(C_COMPILER)
+else
+ CC := gcc
+endif
+
+# Define the command-line options when compiling C files:
+CFLAGS ?= \
+ -std=c99 \
+ -O3 \
+ -Wall \
+ -pedantic
+
+# Determine whether to generate position independent code ([1][1], [2][2]).
+#
+# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options
+# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option
+ifeq ($(OS), WINNT)
+ fPIC ?=
+else
+ fPIC ?= -fPIC
+endif
+
+# List of includes (e.g., `-I /foo/bar -I /beep/boop/include`):
+INCLUDE ?=
+
+# List of source files:
+SOURCE_FILES ?=
+
+# List of libraries (e.g., `-lopenblas -lpthread`):
+LIBRARIES ?=
+
+# List of library paths (e.g., `-L /foo/bar -L /beep/boop`):
+LIBPATH ?=
+
+# List of C targets:
+c_targets := benchmark.out
+
+
+# RULES #
+
+#/
+# Compiles source files.
+#
+# @param {string} [C_COMPILER] - C compiler (e.g., `gcc`)
+# @param {string} [CFLAGS] - C compiler options
+# @param {(string|void)} [fPIC] - compiler flag determining whether to generate position independent code (e.g., `-fPIC`)
+# @param {string} [INCLUDE] - list of includes (e.g., `-I /foo/bar -I /beep/boop/include`)
+# @param {string} [SOURCE_FILES] - list of source files
+# @param {string} [LIBPATH] - list of library paths (e.g., `-L /foo/bar -L /beep/boop`)
+# @param {string} [LIBRARIES] - list of libraries (e.g., `-lopenblas -lpthread`)
+#
+# @example
+# make
+#
+# @example
+# make all
+#/
+all: $(c_targets)
+
+.PHONY: all
+
+#/
+# Compiles C source files.
+#
+# @private
+# @param {string} CC - C compiler (e.g., `gcc`)
+# @param {string} CFLAGS - C compiler options
+# @param {(string|void)} fPIC - compiler flag determining whether to generate position independent code (e.g., `-fPIC`)
+# @param {string} INCLUDE - list of includes (e.g., `-I /foo/bar`)
+# @param {string} SOURCE_FILES - list of source files
+# @param {string} LIBPATH - list of library paths (e.g., `-L /foo/bar`)
+# @param {string} LIBRARIES - list of libraries (e.g., `-lopenblas`)
+#/
+$(c_targets): %.out: %.c
+ $(QUIET) $(CC) $(CFLAGS) $(fPIC) $(INCLUDE) -o $@ $(SOURCE_FILES) $< $(LIBPATH) -lm $(LIBRARIES)
+
+#/
+# Runs compiled benchmarks.
+#
+# @example
+# make run
+#/
+run: $(c_targets)
+ $(QUIET) ./$<
+
+.PHONY: run
+
+#/
+# Removes generated files.
+#
+# @example
+# make clean
+#/
+clean:
+ $(QUIET) -rm -f *.o *.out
+
+.PHONY: clean
diff --git a/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/benchmark/c/benchmark.c b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/benchmark/c/benchmark.c
new file mode 100644
index 000000000000..3a7274f615dc
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/benchmark/c/benchmark.c
@@ -0,0 +1,140 @@
+/**
+* @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.
+*/
+
+#include "stdlib/stats/base/dists/log-logistic/variance.h"
+#include "stdlib/constants/float64/eps.h"
+#include
+#include
+#include
+#include
+#include
+
+#define NAME "log-logistic-variance"
+#define ITERATIONS 1000000
+#define REPEATS 3
+
+/**
+* Prints the TAP version.
+*/
+static void print_version( void ) {
+ printf( "TAP version 13\n" );
+}
+
+/**
+* Prints the TAP summary.
+*
+* @param total total number of tests
+* @param passing total number of passing tests
+*/
+static void print_summary( int total, int passing ) {
+ printf( "#\n" );
+ printf( "1..%d\n", total );
+ printf( "# total %d\n", total );
+ printf( "# pass %d\n", passing );
+ printf( "#\n" );
+ printf( "# ok\n" );
+}
+
+/**
+* Prints benchmarks results.
+*
+* @param elapsed elapsed time in seconds
+*/
+static void print_results( double elapsed ) {
+ double rate = (double)ITERATIONS / elapsed;
+ printf( " ---\n" );
+ printf( " iterations: %d\n", ITERATIONS );
+ printf( " elapsed: %0.9f\n", elapsed );
+ printf( " rate: %0.9f\n", rate );
+ printf( " ...\n" );
+}
+
+/**
+* Returns a clock time.
+*
+* @return clock time
+*/
+static double tic( void ) {
+ struct timeval now;
+ gettimeofday( &now, NULL );
+ return (double)now.tv_sec + (double)now.tv_usec/1.0e6;
+}
+
+/**
+* Generates a random number on the interval [min,max).
+*
+* @param min minimum value (inclusive)
+* @param max maximum value (exclusive)
+* @return random number
+*/
+static double random_uniform( const double min, const double max ) {
+ double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
+ return min + ( v*(max-min) );
+}
+
+/**
+* Runs a benchmark.
+*
+* @return elapsed time in seconds
+*/
+static double benchmark( void ) {
+ double alpha[ 100 ];
+ double beta[ 100 ];
+ double elapsed;
+ double y;
+ double t;
+ int i;
+
+ for ( i = 0; i < 100; i++ ) {
+ alpha[ i ] = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 10.0 );
+ beta[ i ] = random_uniform( 2.1, 10.0 );
+ }
+
+ t = tic();
+ for ( i = 0; i < ITERATIONS; i++ ) {
+ y = stdlib_base_dists_log_logistic_variance( alpha[ i % 100 ], beta[ i % 100 ] );
+ if ( y != y ) {
+ printf( "should not return NaN\n" );
+ break;
+ }
+ }
+ elapsed = tic() - t;
+ if ( y != y ) {
+ printf( "should not return NaN\n" );
+ }
+ return elapsed;
+}
+
+/**
+* Main execution sequence.
+*/
+int main( void ) {
+ double elapsed;
+ int i;
+
+ srand( time( NULL ) );
+
+ print_version();
+ for ( i = 0; i < REPEATS; i++ ) {
+ printf( "# c::%s\n", NAME );
+ elapsed = benchmark();
+ print_results( elapsed );
+ printf( "ok %d benchmark finished\n", i+1 );
+ }
+ print_summary( REPEATS, REPEATS );
+}
diff --git a/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/binding.gyp b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/binding.gyp
new file mode 100644
index 000000000000..0d6508a12e99
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/binding.gyp
@@ -0,0 +1,170 @@
+# @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.
+
+# A `.gyp` file for building a Node.js native add-on.
+#
+# [1]: https://gyp.gsrc.io/docs/InputFormatReference.md
+# [2]: https://gyp.gsrc.io/docs/UserDocumentation.md
+{
+ # List of files to include in this file:
+ 'includes': [
+ './include.gypi',
+ ],
+
+ # Define variables to be used throughout the configuration for all targets:
+ 'variables': {
+ # Target name should match the add-on export name:
+ 'addon_target_name%': 'addon',
+
+ # Set variables based on the host OS:
+ 'conditions': [
+ [
+ 'OS=="win"',
+ {
+ # Define the object file suffix:
+ 'obj': 'obj',
+ },
+ {
+ # Define the object file suffix:
+ 'obj': 'o',
+ }
+ ], # end condition (OS=="win")
+ ], # end conditions
+ }, # end variables
+
+ # Define compile targets:
+ 'targets': [
+
+ # Target to generate an add-on:
+ {
+ # The target name should match the add-on export name:
+ 'target_name': '<(addon_target_name)',
+
+ # Define dependencies:
+ 'dependencies': [],
+
+ # Define directories which contain relevant include headers:
+ 'include_dirs': [
+ # Local include directory:
+ '<@(include_dirs)',
+ ],
+
+ # List of source files:
+ 'sources': [
+ '<@(src_files)',
+ ],
+
+ # Settings which should be applied when a target's object files are used as linker input:
+ 'link_settings': {
+ # Define libraries:
+ 'libraries': [
+ '<@(libraries)',
+ ],
+
+ # Define library directories:
+ 'library_dirs': [
+ '<@(library_dirs)',
+ ],
+ },
+
+ # C/C++ compiler flags:
+ 'cflags': [
+ # Enable commonly used warning options:
+ '-Wall',
+
+ # Aggressive optimization:
+ '-O3',
+ ],
+
+ # C specific compiler flags:
+ 'cflags_c': [
+ # Specify the C standard to which a program is expected to conform:
+ '-std=c99',
+ ],
+
+ # C++ specific compiler flags:
+ 'cflags_cpp': [
+ # Specify the C++ standard to which a program is expected to conform:
+ '-std=c++11',
+ ],
+
+ # Linker flags:
+ 'ldflags': [],
+
+ # Apply conditions based on the host OS:
+ 'conditions': [
+ [
+ 'OS=="mac"',
+ {
+ # Linker flags:
+ 'ldflags': [
+ '-undefined dynamic_lookup',
+ '-Wl,-no-pie',
+ '-Wl,-search_paths_first',
+ ],
+ },
+ ], # end condition (OS=="mac")
+ [
+ 'OS!="win"',
+ {
+ # C/C++ flags:
+ 'cflags': [
+ # Generate platform-independent code:
+ '-fPIC',
+ ],
+ },
+ ], # end condition (OS!="win")
+ ], # end conditions
+ }, # end target <(addon_target_name)
+
+ # Target to copy a generated add-on to a standard location:
+ {
+ 'target_name': 'copy_addon',
+
+ # Declare that the output of this target is not linked:
+ 'type': 'none',
+
+ # Define dependencies:
+ 'dependencies': [
+ # Require that the add-on be generated before building this target:
+ '<(addon_target_name)',
+ ],
+
+ # Define a list of actions:
+ 'actions': [
+ {
+ 'action_name': 'copy_addon',
+ 'message': 'Copying addon...',
+
+ # Explicitly list the inputs in the command-line invocation below:
+ 'inputs': [],
+
+ # Declare the expected outputs:
+ 'outputs': [
+ '<(addon_output_dir)/<(addon_target_name).node',
+ ],
+
+ # Define the command-line invocation:
+ 'action': [
+ 'cp',
+ '<(PRODUCT_DIR)/<(addon_target_name).node',
+ '<(addon_output_dir)/<(addon_target_name).node',
+ ],
+ },
+ ], # end actions
+ }, # end target copy_addon
+ ], # end targets
+}
diff --git a/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/docs/repl.txt b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/docs/repl.txt
new file mode 100644
index 000000000000..09476d506ccb
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/docs/repl.txt
@@ -0,0 +1,44 @@
+
+{{alias}}( α, β )
+ Returns the variance of a log-logistic distribution with scale parameter
+ `α` and shape parameter `β`.
+
+ If provided `NaN` as any argument, the function returns `NaN`.
+
+ If provided `α <= 0`, the function returns `NaN`.
+
+ If provided `β <= 2`, the function returns `NaN`.
+
+ Parameters
+ ----------
+ α: number
+ Scale parameter.
+
+ β: number
+ Shape parameter.
+
+ Returns
+ -------
+ out: number
+ Variance.
+
+ Examples
+ --------
+ > var y = {{alias}}( 1.0, 3.0 )
+ ~0.956
+ > y = {{alias}}( 4.0, 3.0 )
+ ~15.300
+ > y = {{alias}}( 1.0, 2.0 )
+ NaN
+ > y = {{alias}}( NaN, 3.0 )
+ NaN
+ > y = {{alias}}( 2.0, NaN )
+ NaN
+ > y = {{alias}}( -1.0, 3.0 )
+ NaN
+ > y = {{alias}}( 2.0, -1.0 )
+ NaN
+
+ See Also
+ --------
+
diff --git a/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/docs/types/index.d.ts b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/docs/types/index.d.ts
new file mode 100644
index 000000000000..f6b356ab5b6a
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/docs/types/index.d.ts
@@ -0,0 +1,66 @@
+/*
+* @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
+
+/**
+* Returns the variance of a log-logistic distribution with scale parameter `alpha` and shape parameter `beta`.
+*
+* ## Notes
+*
+* - If provided `alpha <= 0`, the function returns `NaN`.
+* - If provided `beta <= 2`, the function returns `NaN`.
+*
+* @param alpha - scale parameter
+* @param beta - shape parameter
+* @returns variance
+*
+* @example
+* var y = variance( 1.0, 3.0 );
+* // returns ~0.956
+*
+* @example
+* var y = variance( 4.0, 3.0 );
+* // returns ~15.300
+*
+* @example
+* var y = variance( 1.0, 2.0 );
+* // returns NaN
+*
+* @example
+* var y = variance( NaN, 3.0 );
+* // returns NaN
+*
+* @example
+* var y = variance( 2.0, NaN );
+* // returns NaN
+*
+* @example
+* var y = variance( -1.0, 3.0 );
+* // returns NaN
+*
+* @example
+* var y = variance( 2.0, -1.0 );
+* // returns NaN
+*/
+declare function variance( alpha: number, beta: number ): number;
+
+
+// EXPORTS //
+
+export = variance;
diff --git a/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/docs/types/test.ts b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/docs/types/test.ts
new file mode 100644
index 000000000000..8610f73ed9f5
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/docs/types/test.ts
@@ -0,0 +1,56 @@
+/*
+* @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 variance = require( './index' );
+
+
+// TESTS //
+
+// The function returns a number...
+{
+ variance( 1.0, 3.0 ); // $ExpectType number
+}
+
+// The compiler throws an error if the function is provided values other than two numbers...
+{
+ variance( true, 3 ); // $ExpectError
+ variance( false, 2 ); // $ExpectError
+ variance( '5', 1 ); // $ExpectError
+ variance( [], 1 ); // $ExpectError
+ variance( {}, 2 ); // $ExpectError
+ variance( ( x: number ): number => x, 2 ); // $ExpectError
+
+ variance( 9, true ); // $ExpectError
+ variance( 9, false ); // $ExpectError
+ variance( 5, '5' ); // $ExpectError
+ variance( 8, [] ); // $ExpectError
+ variance( 9, {} ); // $ExpectError
+ variance( 8, ( x: number ): number => x ); // $ExpectError
+
+ variance( [], true ); // $ExpectError
+ variance( {}, false ); // $ExpectError
+ variance( false, '5' ); // $ExpectError
+ variance( {}, [] ); // $ExpectError
+ variance( '5', ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided insufficient arguments...
+{
+ variance(); // $ExpectError
+ variance( 3 ); // $ExpectError
+}
diff --git a/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/examples/c/Makefile b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/examples/c/Makefile
new file mode 100644
index 000000000000..c8f8e9a1517b
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/examples/c/Makefile
@@ -0,0 +1,146 @@
+#/
+# @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.
+#/
+
+# VARIABLES #
+
+ifndef VERBOSE
+ QUIET := @
+else
+ QUIET :=
+endif
+
+# Determine the OS ([1][1], [2][2]).
+#
+# [1]: https://en.wikipedia.org/wiki/Uname#Examples
+# [2]: http://stackoverflow.com/a/27776822/2225624
+OS ?= $(shell uname)
+ifneq (, $(findstring MINGW,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring MSYS,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring CYGWIN,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring Windows_NT,$(OS)))
+ OS := WINNT
+endif
+endif
+endif
+endif
+
+# Define the program used for compiling C source files:
+ifdef C_COMPILER
+ CC := $(C_COMPILER)
+else
+ CC := gcc
+endif
+
+# Define the command-line options when compiling C files:
+CFLAGS ?= \
+ -std=c99 \
+ -O3 \
+ -Wall \
+ -pedantic
+
+# Determine whether to generate position independent code ([1][1], [2][2]).
+#
+# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options
+# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option
+ifeq ($(OS), WINNT)
+ fPIC ?=
+else
+ fPIC ?= -fPIC
+endif
+
+# List of includes (e.g., `-I /foo/bar -I /beep/boop/include`):
+INCLUDE ?=
+
+# List of source files:
+SOURCE_FILES ?=
+
+# List of libraries (e.g., `-lopenblas -lpthread`):
+LIBRARIES ?=
+
+# List of library paths (e.g., `-L /foo/bar -L /beep/boop`):
+LIBPATH ?=
+
+# List of C targets:
+c_targets := example.out
+
+
+# RULES #
+
+#/
+# Compiles source files.
+#
+# @param {string} [C_COMPILER] - C compiler (e.g., `gcc`)
+# @param {string} [CFLAGS] - C compiler options
+# @param {(string|void)} [fPIC] - compiler flag determining whether to generate position independent code (e.g., `-fPIC`)
+# @param {string} [INCLUDE] - list of includes (e.g., `-I /foo/bar -I /beep/boop/include`)
+# @param {string} [SOURCE_FILES] - list of source files
+# @param {string} [LIBPATH] - list of library paths (e.g., `-L /foo/bar -L /beep/boop`)
+# @param {string} [LIBRARIES] - list of libraries (e.g., `-lopenblas -lpthread`)
+#
+# @example
+# make
+#
+# @example
+# make all
+#/
+all: $(c_targets)
+
+.PHONY: all
+
+#/
+# Compiles C source files.
+#
+# @private
+# @param {string} CC - C compiler (e.g., `gcc`)
+# @param {string} CFLAGS - C compiler options
+# @param {(string|void)} fPIC - compiler flag determining whether to generate position independent code (e.g., `-fPIC`)
+# @param {string} INCLUDE - list of includes (e.g., `-I /foo/bar`)
+# @param {string} SOURCE_FILES - list of source files
+# @param {string} LIBPATH - list of library paths (e.g., `-L /foo/bar`)
+# @param {string} LIBRARIES - list of libraries (e.g., `-lopenblas`)
+#/
+$(c_targets): %.out: %.c
+ $(QUIET) $(CC) $(CFLAGS) $(fPIC) $(INCLUDE) -o $@ $(SOURCE_FILES) $< $(LIBPATH) -lm $(LIBRARIES)
+
+#/
+# Runs compiled examples.
+#
+# @example
+# make run
+#/
+run: $(c_targets)
+ $(QUIET) ./$<
+
+.PHONY: run
+
+#/
+# Removes generated files.
+#
+# @example
+# make clean
+#/
+clean:
+ $(QUIET) -rm -f *.o *.out
+
+.PHONY: clean
diff --git a/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/examples/c/example.c b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/examples/c/example.c
new file mode 100644
index 000000000000..422eb2335ce2
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/examples/c/example.c
@@ -0,0 +1,40 @@
+/**
+* @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.
+*/
+
+#include "stdlib/stats/base/dists/log-logistic/variance.h"
+#include
+#include
+
+static double random_uniform( const double min, const double max ) {
+ double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
+ return min + ( v*(max-min) );
+}
+
+int main( void ) {
+ double alpha;
+ double beta;
+ double v;
+ int i;
+
+ for ( i = 0; i < 25; i++ ) {
+ alpha = random_uniform( 0.1, 10.0 );
+ beta = random_uniform( 2.1, 10.0 );
+ v = stdlib_base_dists_log_logistic_variance( alpha, beta );
+ printf( "α: %lf, β: %lf, Var(X;α,β): %lf\n", alpha, beta, v );
+ }
+}
diff --git a/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/examples/index.js b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/examples/index.js
new file mode 100644
index 000000000000..6647d9459bb1
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/examples/index.js
@@ -0,0 +1,31 @@
+/**
+* @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/array/uniform' );
+var logEachMap = require( '@stdlib/console/log-each-map' );
+var variance = require( './../lib' );
+
+var opts = {
+ 'dtype': 'float64'
+};
+var alpha = uniform( 10, 0.1, 10.0, opts );
+var beta = uniform( 10, 2.1, 10.0, opts );
+
+logEachMap( 'α: %0.4f, β: %0.4f, Var(X;α,β): %0.4f', alpha, beta, variance );
diff --git a/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/include.gypi b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/include.gypi
new file mode 100644
index 000000000000..bee8d41a2caf
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/include.gypi
@@ -0,0 +1,53 @@
+# @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.
+
+# A GYP include file for building a Node.js native add-on.
+#
+# Main documentation:
+#
+# [1]: https://gyp.gsrc.io/docs/InputFormatReference.md
+# [2]: https://gyp.gsrc.io/docs/UserDocumentation.md
+{
+ # Define variables to be used throughout the configuration for all targets:
+ 'variables': {
+ # Source directory:
+ 'src_dir': './src',
+
+ # Include directories:
+ 'include_dirs': [
+ '=0.10.0",
+ "npm": ">2.7.0"
+ },
+ "os": [
+ "aix",
+ "darwin",
+ "freebsd",
+ "linux",
+ "macos",
+ "openbsd",
+ "sunos",
+ "win32",
+ "windows"
+ ],
+ "keywords": [
+ "stdlib",
+ "stdmath",
+ "statistics",
+ "stats",
+ "distribution",
+ "dist",
+ "moments",
+ "continuous",
+ "variance",
+ "var",
+ "dispersion",
+ "log-logistic",
+ "univariate"
+ ]
+}
diff --git a/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/src/Makefile b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/src/Makefile
new file mode 100644
index 000000000000..2caf905cedbe
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/src/Makefile
@@ -0,0 +1,70 @@
+#/
+# @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.
+#/
+
+# VARIABLES #
+
+ifndef VERBOSE
+ QUIET := @
+else
+ QUIET :=
+endif
+
+# Determine the OS ([1][1], [2][2]).
+#
+# [1]: https://en.wikipedia.org/wiki/Uname#Examples
+# [2]: http://stackoverflow.com/a/27776822/2225624
+OS ?= $(shell uname)
+ifneq (, $(findstring MINGW,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring MSYS,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring CYGWIN,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring Windows_NT,$(OS)))
+ OS := WINNT
+endif
+endif
+endif
+endif
+
+
+# RULES #
+
+#/
+# Removes generated files for building an add-on.
+#
+# @example
+# make clean-addon
+#/
+clean-addon:
+ $(QUIET) -rm -f *.o *.node
+
+.PHONY: clean-addon
+
+#/
+# Removes generated files.
+#
+# @example
+# make clean
+#/
+clean: clean-addon
+
+.PHONY: clean
diff --git a/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/src/addon.c b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/src/addon.c
new file mode 100644
index 000000000000..be45b8cfe331
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/src/addon.c
@@ -0,0 +1,22 @@
+/**
+* @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.
+*/
+
+#include "stdlib/stats/base/dists/log-logistic/variance.h"
+#include "stdlib/math/base/napi/binary.h"
+
+STDLIB_MATH_BASE_NAPI_MODULE_DD_D( stdlib_base_dists_log_logistic_variance )
diff --git a/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/src/main.c b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/src/main.c
new file mode 100644
index 000000000000..8b5be4bd39e3
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/src/main.c
@@ -0,0 +1,51 @@
+/**
+* @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.
+*/
+
+#include "stdlib/stats/base/dists/log-logistic/variance.h"
+#include "stdlib/math/base/assert/is_nan.h"
+#include "stdlib/math/base/special/sin.h"
+#include "stdlib/constants/float64/pi.h"
+
+/**
+* Returns the variance of a log-logistic distribution with scale parameter `alpha` and shape parameter `beta`.
+*
+* @param alpha scale parameter
+* @param beta shape parameter
+* @return variance
+*
+* @example
+* double v = stdlib_base_dists_log_logistic_variance( 1.0, 3.0 );
+* // returns ~0.956
+*/
+double stdlib_base_dists_log_logistic_variance( const double alpha, const double beta ) {
+ double b2;
+ double b;
+ double s;
+ if (
+ stdlib_base_is_nan( alpha ) ||
+ stdlib_base_is_nan( beta ) ||
+ alpha <= 0.0 ||
+ beta <= 2.0
+ ) {
+ return 0.0 / 0.0; // NaN
+ }
+ b = STDLIB_CONSTANT_FLOAT64_PI / beta;
+ b2 = 2.0 * b;
+ s = stdlib_base_sin( b );
+ return ( alpha * alpha ) * ( ( b2 / stdlib_base_sin( b2 ) ) - ( ( b * b ) / ( s * s ) ) );
+}
diff --git a/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/test/fixtures/julia/REQUIRE b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/test/fixtures/julia/REQUIRE
new file mode 100644
index 000000000000..98be20b58ed3
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/test/fixtures/julia/REQUIRE
@@ -0,0 +1,3 @@
+Distributions 0.23.8
+julia 1.5
+JSON 0.21
diff --git a/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/test/fixtures/julia/data.json b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/test/fixtures/julia/data.json
new file mode 100644
index 000000000000..1d14150248d0
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/test/fixtures/julia/data.json
@@ -0,0 +1 @@
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diff --git a/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/test/fixtures/julia/runner.jl
new file mode 100644
index 000000000000..eff2ed31a5f0
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/test/fixtures/julia/runner.jl
@@ -0,0 +1,72 @@
+#!/usr/bin/env julia
+#
+# @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 Distributions: var, LogLogistic
+import JSON
+
+"""
+ gen( alpha, beta, name )
+
+Generate fixture data and write to file.
+
+# Arguments
+
+* `alpha`: scale parameter
+* `beta`: shape parameter
+* `name::AbstractString`: output filename
+
+# Examples
+``` julia
+julia> alpha = rand( 1000 ) .* 10.0 .+ 0.1;
+julia> beta = rand( 1000 ) .* 8.0 .+ 2.1;
+julia> gen( alpha, beta, "data.json" );
+```
+"""
+function gen( alpha, beta, name )
+ z = Array{Float64}( undef, length(alpha) );
+ for i in eachindex(alpha)
+ z[ i ] = var( LogLogistic( alpha[i], beta[i] ) );
+ end
+
+ # Store data to be written to file as a collection:
+ data = Dict([
+ ("alpha", alpha),
+ ("beta", beta),
+ ("expected", z)
+ ]);
+
+ # Based on the script directory, create an output filepath:
+ filepath = joinpath( dir, name );
+
+ # Write the data to the output filepath as JSON:
+ outfile = open( filepath, "w" );
+ write( outfile, JSON.json(data) );
+ write( outfile, "\n" );
+ close( outfile );
+end
+
+# Get the filename:
+file = @__FILE__;
+
+# Extract the directory in which this file resides:
+dir = dirname( file );
+
+# Generate fixtures:
+alpha = ( rand( 1000 ) .* 10.0 ) .+ 0.1;
+beta = ( rand( 1000 ) .* 8.0 ) .+ 2.1;
+gen( alpha, beta, "data.json" );
diff --git a/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/test/test.js b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/test/test.js
new file mode 100644
index 000000000000..f6f8f6bad41a
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/test/test.js
@@ -0,0 +1,118 @@
+/**
+* @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 isnan = require( '@stdlib/math/base/assert/is-nan' );
+var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' );
+var PINF = require( '@stdlib/constants/float64/pinf' );
+var NINF = require( '@stdlib/constants/float64/ninf' );
+var variance = require( './../lib' );
+
+
+// FIXTURES //
+
+var data = require( './fixtures/julia/data.json' );
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+ t.ok( true, __filename );
+ t.strictEqual( typeof variance, 'function', 'main export is a function' );
+ t.end();
+});
+
+tape( 'if provided `NaN` for any parameter, the function returns `NaN`', function test( t ) {
+ var y = variance( NaN, 3.0 );
+ t.strictEqual( isnan( y ), true, 'returns expected value' );
+ y = variance( 1.0, NaN );
+ t.strictEqual( isnan( y ), true, 'returns expected value' );
+ t.end();
+});
+
+tape( 'if provided a nonpositive `alpha`, the function returns `NaN`', function test( t ) {
+ var y;
+
+ y = variance( 0.0, 3.0 );
+ t.strictEqual( isnan( y ), true, 'returns expected value' );
+
+ y = variance( -1.0, 3.0 );
+ t.strictEqual( isnan( y ), true, 'returns expected value' );
+
+ y = variance( NINF, 3.0 );
+ t.strictEqual( isnan( y ), true, 'returns expected value' );
+
+ t.end();
+});
+
+tape( 'if provided a nonpositive `beta`, the function returns `NaN`', function test( t ) {
+ var y;
+
+ y = variance( 2.0, 0.0 );
+ t.strictEqual( isnan( y ), true, 'returns expected value' );
+
+ y = variance( 2.0, -1.0 );
+ t.strictEqual( isnan( y ), true, 'returns expected value' );
+
+ y = variance( 1.0, NINF );
+ t.strictEqual( isnan( y ), true, 'returns expected value' );
+
+ y = variance( PINF, NINF );
+ t.strictEqual( isnan( y ), true, 'returns expected value' );
+
+ y = variance( NINF, NINF );
+ t.strictEqual( isnan( y ), true, 'returns expected value' );
+
+ y = variance( NaN, NINF );
+ t.strictEqual( isnan( y ), true, 'returns expected value' );
+
+ t.end();
+});
+
+tape( 'if provided `beta <= 2`, the function returns `NaN`', function test( t ) {
+ var y;
+
+ y = variance( 2.0, 2.0 );
+ t.strictEqual( isnan( y ), true, 'returns expected value' );
+
+ y = variance( 2.0, 1.5 );
+ t.strictEqual( isnan( y ), true, 'returns expected value' );
+
+ t.end();
+});
+
+tape( 'the function returns the variance of a log-logistic distribution', function test( t ) {
+ var expected;
+ var alpha;
+ var beta;
+ var y;
+ var i;
+
+ expected = data.expected;
+ alpha = data.alpha;
+ beta = data.beta;
+ for ( i = 0; i < alpha.length; i++ ) {
+ y = variance( alpha[ i ], beta[ i ] );
+ t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' );
+ }
+ t.end();
+});
diff --git a/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/test/test.native.js b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/test/test.native.js
new file mode 100644
index 000000000000..a47f50171843
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/log-logistic/variance/test/test.native.js
@@ -0,0 +1,127 @@
+/**
+* @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 resolve = require( 'path' ).resolve;
+var tape = require( 'tape' );
+var tryRequire = require( '@stdlib/utils/try-require' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' );
+var PINF = require( '@stdlib/constants/float64/pinf' );
+var NINF = require( '@stdlib/constants/float64/ninf' );
+
+
+// VARIABLES //
+
+var variance = tryRequire( resolve( __dirname, './../lib/native.js' ) );
+var opts = {
+ 'skip': ( variance instanceof Error )
+};
+
+
+// FIXTURES //
+
+var data = require( './fixtures/julia/data.json' );
+
+
+// TESTS //
+
+tape( 'main export is a function', opts, function test( t ) {
+ t.ok( true, __filename );
+ t.strictEqual( typeof variance, 'function', 'main export is a function' );
+ t.end();
+});
+
+tape( 'if provided `NaN` for any parameter, the function returns `NaN`', opts, function test( t ) {
+ var y = variance( NaN, 3.0 );
+ t.strictEqual( isnan( y ), true, 'returns expected value' );
+ y = variance( 1.0, NaN );
+ t.strictEqual( isnan( y ), true, 'returns expected value' );
+ t.end();
+});
+
+tape( 'if provided a nonpositive `alpha`, the function returns `NaN`', opts, function test( t ) {
+ var y;
+
+ y = variance( 0.0, 3.0 );
+ t.strictEqual( isnan( y ), true, 'returns expected value' );
+
+ y = variance( -1.0, 3.0 );
+ t.strictEqual( isnan( y ), true, 'returns expected value' );
+
+ y = variance( NINF, 3.0 );
+ t.strictEqual( isnan( y ), true, 'returns expected value' );
+
+ t.end();
+});
+
+tape( 'if provided a nonpositive `beta`, the function returns `NaN`', opts, function test( t ) {
+ var y;
+
+ y = variance( 2.0, 0.0 );
+ t.strictEqual( isnan( y ), true, 'returns expected value' );
+
+ y = variance( 2.0, -1.0 );
+ t.strictEqual( isnan( y ), true, 'returns expected value' );
+
+ y = variance( 1.0, NINF );
+ t.strictEqual( isnan( y ), true, 'returns expected value' );
+
+ y = variance( PINF, NINF );
+ t.strictEqual( isnan( y ), true, 'returns expected value' );
+
+ y = variance( NINF, NINF );
+ t.strictEqual( isnan( y ), true, 'returns expected value' );
+
+ y = variance( NaN, NINF );
+ t.strictEqual( isnan( y ), true, 'returns expected value' );
+
+ t.end();
+});
+
+tape( 'if provided `beta <= 2`, the function returns `NaN`', opts, function test( t ) {
+ var y;
+
+ y = variance( 2.0, 2.0 );
+ t.strictEqual( isnan( y ), true, 'returns expected value' );
+
+ y = variance( 2.0, 1.5 );
+ t.strictEqual( isnan( y ), true, 'returns expected value' );
+
+ t.end();
+});
+
+tape( 'the function returns the variance of a log-logistic distribution', opts, function test( t ) {
+ var expected;
+ var alpha;
+ var beta;
+ var y;
+ var i;
+
+ expected = data.expected;
+ alpha = data.alpha;
+ beta = data.beta;
+ for ( i = 0; i < alpha.length; i++ ) {
+ y = variance( alpha[ i ], beta[ i ] );
+ t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'returns expected value' );
+ }
+ t.end();
+});