diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/README.md b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/README.md
new file mode 100644
index 000000000000..c0230d074d18
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/README.md
@@ -0,0 +1,157 @@
+
+
+# Moment-Generating Function
+
+> Planck (discrete exponential) distribution moment-generating function (MGF).
+
+
+
+
+
+The [moment-generating function][mgf] for a Planck random variable is
+
+
+
+```math
+M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = \frac{1 - e^{-\lambda}}{1 - e^{t - \lambda}}
+```
+
+
+
+where `λ` is the shape parameter.
+
+
+
+
+
+
+
+
+
+## Usage
+
+```javascript
+var mgf = require( '@stdlib/stats/base/dists/planck/mgf' );
+```
+
+#### mgf( t, lambda )
+
+Evaluates the moment-generating function ([MGF][mgf]) of a Planck (discrete exponential) distribution with shape parameter `lambda`.
+
+```javascript
+var y = mgf( 0.2, 0.5 );
+// returns ~1.5181
+
+y = mgf( 0.4, 1.5 );
+// returns ~1.1645
+```
+
+If provided `NaN` as any argument, the function returns `NaN`.
+
+```javascript
+var y = mgf( NaN, 0.0 );
+// returns NaN
+
+y = mgf( 0.0, NaN );
+// returns NaN
+```
+
+If provided a shape parameter `lambda` which is nonpositive, the function returns `NaN`.
+
+```javascript
+var y = mgf( 2.0, -1.0 );
+// returns NaN
+```
+
+#### mgf.factory( lambda )
+
+Returns a function for evaluating the [moment-generating function][mgf] of a Planck (discrete exponential) distribution with shape parameter `lambda`.
+
+```javascript
+var mymgf = mgf.factory( 0.8 );
+var y = mymgf( -0.2 );
+// returns ~0.8711
+```
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+## Examples
+
+
+
+```javascript
+var uniform = require( '@stdlib/random/array/uniform' );
+var mgf = require( '@stdlib/stats/base/dists/planck/mgf' );
+
+var lambda = uniform( 10, 0.1, 5.0 );
+var t = uniform( 10, 0.0, 10.0 );
+
+var y;
+var i;
+for ( i = 0; i < lambda.length; i++ ) {
+ y = mgf( t[ i ], lambda[ i ] );
+ console.log( 't: %d, λ: %d, M_X(t;λ): %d', t[ i ].toFixed( 4 ), lambda[ i ].toFixed( 4 ), y.toFixed( 4 ) );
+}
+```
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+[mgf]: https://en.wikipedia.org/wiki/Moment-generating_function
+
+
+
+
diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/benchmark/benchmark.js b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/benchmark/benchmark.js
new file mode 100644
index 000000000000..f40aad933643
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/benchmark/benchmark.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';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pkg = require( './../package.json' ).name;
+var mgf = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+ var lambda;
+ var t;
+ var y;
+ var i;
+
+ lambda = uniform( 100, 0.1, 10.0 );
+ t = uniform( 100, 0.0, 10.0 );
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ y = mgf( t[ i % t.length ], lambda[ i % lambda.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();
+});
+
+bench( pkg+':factory', function benchmark( b ) {
+ var mymgf;
+ var t;
+ var y;
+ var i;
+
+ t = uniform( 100, 0.0, 10.0 );
+ mymgf = mgf.factory( 0.3 );
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ y = mymgf( t[ i % t.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/planck/mgf/docs/repl.txt b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/docs/repl.txt
new file mode 100644
index 000000000000..f628063e0fdf
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/docs/repl.txt
@@ -0,0 +1,59 @@
+
+{{alias}}( t, λ )
+ Evaluates the moment-generating function (MGF) for a Planck distribution
+ with shape parameter `λ` at a value `t`.
+
+ If provided `NaN` as any argument, the function returns `NaN`.
+
+ If `λ <= 0`, the function returns `NaN`.
+
+ Parameters
+ ----------
+ t: number
+ Input value.
+
+ λ: number
+ Shape parameter.
+
+ Returns
+ -------
+ out: number
+ Evaluated MGF.
+
+ Examples
+ --------
+ > var y = {{alias}}( 0.2, 0.5 )
+ ~1.5181
+ > y = {{alias}}( 0.4, 1.5 )
+ ~1.1645
+ > y = {{alias}}( NaN, 0.0 )
+ NaN
+ > y = {{alias}}( 0.0, NaN )
+ NaN
+ > y = {{alias}}( 2.0, -1.0 )
+ NaN
+
+
+{{alias}}.factory( λ )
+ Returns a function for evaluating the moment-generating function (MGF) of a
+ Planck distribution with shape parameter `λ`.
+
+ Parameters
+ ----------
+ λ: number
+ Shape parameter.
+
+ Returns
+ -------
+ mgf: Function
+ Moment-generating function (MGF).
+
+ Examples
+ --------
+ > var mymgf = {{alias}}.factory( 0.8 );
+ > var y = mymgf( -0.2 )
+ ~0.8711
+
+ See Also
+ --------
+
diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/docs/types/index.d.ts b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/docs/types/index.d.ts
new file mode 100644
index 000000000000..74eff51f795d
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/docs/types/index.d.ts
@@ -0,0 +1,103 @@
+/*
+* @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
+
+/**
+* Evaluates the moment-generating function (MGF) of a Planck distribution.
+*
+* @param t - input value
+* @returns evaluated MGF
+*/
+type Unary = ( t: number ) => number;
+
+/**
+* Interface for the moment-generating function (MGF) of a Planck distribution.
+*/
+interface MGF {
+ /**
+ * Evaluates the moment-generating function (MGF) for a Planck distribution with shape parameter `lambda` at a value `t`.
+ *
+ * ## Notes
+ *
+ * - If `lambda <= 0`, the function returns `NaN`.
+ *
+ * @param t - input value
+ * @param lambda - shape parameter
+ * @returns evaluated MGF
+ *
+ * @example
+ * var y = mgf( 0.2, 0.5 );
+ * // returns ~1.5181
+ *
+ * @example
+ * var y = mgf( 0.4, 1.5 );
+ * // returns ~1.1645
+ *
+ * @example
+ * var y = mgf( NaN, 0.0 );
+ * // returns NaN
+ *
+ * @example
+ * var y = mgf( 0.0, NaN );
+ * // returns NaN
+ *
+ * @example
+ * var y = mgf( 2.0, -1.0 );
+ * // returns NaN
+ */
+ ( t: number, lambda: number ): number;
+
+ /**
+ * Returns a function for evaluating the moment-generating function (MGF) of a Planck distribution with shape parameter `lambda`.
+ *
+ * @param lambda - shape parameter
+ * @returns MGF
+ *
+ * @example
+ * var mymgf = mgf.factory( 0.8 );
+ * var y = mymgf( -0.2 );
+ * // returns ~0.8711
+ */
+ factory( lambda: number ): Unary;
+}
+
+/**
+* Planck distribution moment-generating function (MGF).
+*
+* @param t - input value
+* @param lambda - shape parameter
+* @returns evaluated MGF
+*
+* @example
+* var y = mgf( 0.2, 0.5 );
+* // returns ~1.5181
+*
+* y = mgf( 0.4, 1.5 );
+* // returns ~1.1645
+*
+* var mymgf = mgf.factory( 0.8 );
+* y = mymgf( -0.2 );
+* // returns ~0.8711
+*/
+declare var mgf: MGF;
+
+
+// EXPORTS //
+
+export = mgf;
diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/docs/types/test.ts b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/docs/types/test.ts
new file mode 100644
index 000000000000..e80a2a7bc4fa
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/docs/types/test.ts
@@ -0,0 +1,98 @@
+/*
+* @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.
+*/
+
+import mgf = require( './index' );
+
+
+// TESTS //
+
+// The function returns a number...
+{
+ mgf( 2.0, 0.4 ); // $ExpectType number
+ mgf( 1.0, 0.2 ); // $ExpectType number
+}
+
+// The compiler throws an error if the function is provided values other than two numbers...
+{
+ mgf( true, 0.3 ); // $ExpectError
+ mgf( false, 0.2 ); // $ExpectError
+ mgf( '5', 0.1 ); // $ExpectError
+ mgf( [], 0.1 ); // $ExpectError
+ mgf( {}, 0.4 ); // $ExpectError
+ mgf( ( x: number ): number => x, 0.2 ); // $ExpectError
+
+ mgf( 9.0, true ); // $ExpectError
+ mgf( 9.0, false ); // $ExpectError
+ mgf( 5.0, '5' ); // $ExpectError
+ mgf( 8.0, [] ); // $ExpectError
+ mgf( 9.0, {} ); // $ExpectError
+ mgf( 8.0, ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided an unsupported number of arguments...
+{
+ mgf(); // $ExpectError
+ mgf( 2.0 ); // $ExpectError
+ mgf( 2.0, 0.8, 4.0 ); // $ExpectError
+}
+
+// Attached to main export is a `factory` method which returns a function...
+{
+ mgf.factory( 0.4 ); // $ExpectType Unary
+}
+
+// The `factory` method returns a function which returns a number...
+{
+ const fcn = mgf.factory( 0.4 );
+ fcn( 2.0 ); // $ExpectType number
+}
+
+// The compiler throws an error if the function returned by the `factory` method is provided an invalid argument...
+{
+ const fcn = mgf.factory( 0.4 );
+ fcn( true ); // $ExpectError
+ fcn( false ); // $ExpectError
+ fcn( '5' ); // $ExpectError
+ fcn( [] ); // $ExpectError
+ fcn( {} ); // $ExpectError
+ fcn( ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the function returned by the `factory` method is provided an unsupported number of arguments...
+{
+ const fcn = mgf.factory( 0.4 );
+ fcn(); // $ExpectError
+ fcn( 2.0, 0.8 ); // $ExpectError
+ fcn( 2.0, 0.9, 1.0 ); // $ExpectError
+}
+
+// The compiler throws an error if the `factory` method is provided a value other than a number...
+{
+ mgf.factory( true ); // $ExpectError
+ mgf.factory( false ); // $ExpectError
+ mgf.factory( '5' ); // $ExpectError
+ mgf.factory( [] ); // $ExpectError
+ mgf.factory( {} ); // $ExpectError
+ mgf.factory( ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the `factory` method is provided an unsupported number of arguments...
+{
+ mgf.factory( 0.9, 0.2 ); // $ExpectError
+ mgf.factory( 0.8, 0.4, 8.0 ); // $ExpectError
+}
diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/examples/index.js b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/examples/index.js
new file mode 100644
index 000000000000..dc49b4e37075
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/examples/index.js
@@ -0,0 +1,32 @@
+/**
+* @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 uniform = require( '@stdlib/random/array/uniform' );
+var mgf = require( './../lib' );
+
+var lambda = uniform( 10, 0.1, 5.0 );
+var t = uniform( 10, 0.0, 10.0 );
+
+var y;
+var i;
+for ( i = 0; i < lambda.length; i++ ) {
+ y = mgf( t[ i ], lambda[ i ] );
+ console.log( 't: %d, λ: %d, M_X(t;λ): %d', t[ i ].toFixed( 4 ), lambda[ i ].toFixed( 4 ), y.toFixed( 4 ) );
+}
diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/lib/factory.js b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/lib/factory.js
new file mode 100644
index 000000000000..c8d6031767d0
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/lib/factory.js
@@ -0,0 +1,69 @@
+/**
+* @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 constantFunction = require( '@stdlib/utils/constant-function' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var expm1 = require( '@stdlib/math/base/special/expm1' );
+
+
+// MAIN //
+
+/**
+* Returns a function for evaluating the moment-generating function (MGF) of a Planck distribution with shape parameter `lambda`.
+*
+* @param {PositiveNumber} lambda - shape parameter
+* @returns {Function} MGF
+*
+* @example
+* var mgf = factory( 0.8 );
+* var y = mgf( -0.2 );
+* // returns ~0.8711
+*/
+function factory( lambda ) {
+ if ( isnan( lambda ) || lambda <= 0.0 ) {
+ return constantFunction( NaN );
+ }
+ return mgf;
+
+ /**
+ * Evaluates the moment-generating function (MGF) for a Planck distribution.
+ *
+ * @private
+ * @param {number} t - input value
+ * @returns {number} evaluated MGF
+ *
+ * @example
+ * var y = mgf( 0.5 );
+ * // returns
+ */
+ function mgf( t ) {
+ if ( isnan( t ) ) {
+ return NaN;
+ }
+ return expm1( -lambda ) / expm1( t - lambda );
+ }
+}
+
+
+// EXPORTS //
+
+module.exports = factory;
diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/lib/index.js b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/lib/index.js
new file mode 100644
index 000000000000..363a2cd6081b
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/lib/index.js
@@ -0,0 +1,54 @@
+/**
+* @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';
+
+/**
+* Evaluate the moment-generating function (MGF) for a Planck distribution.
+*
+* @module @stdlib/stats/base/dists/planck/mgf
+*
+* @example
+* var mgf = require( '@stdlib/stats/base/dists/planck/mgf' );
+*
+* var y = mgf( 0.2, 0.5 );
+* // returns ~1.5181
+*
+* y = mgf( 0.4, 1.5 );
+* // returns ~1.1645
+*
+* var mymgf = mgf.factory( 0.8 );
+* y = mymgf( -0.2 );
+* // returns ~0.8711
+*/
+
+// MODULES //
+
+var setReadOnly = require( '@stdlib/utils/define-nonenumerable-read-only-property' );
+var main = require( './main.js' );
+var factory = require( './factory.js' );
+
+
+// MAIN //
+
+setReadOnly( main, 'factory', factory );
+
+
+// EXPORTS //
+
+module.exports = main;
diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/lib/main.js b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/lib/main.js
new file mode 100644
index 000000000000..3c9742edf52d
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/lib/main.js
@@ -0,0 +1,66 @@
+/**
+* @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 isnan = require( '@stdlib/math/base/assert/is-nan' );
+var expm1 = require( '@stdlib/math/base/special/expm1' );
+
+
+// MAIN //
+
+/**
+* Evaluates the moment-generating function (MGF) for a Planck distribution with shape parameter `lambda` at a value `t`.
+*
+* @param {number} t - input value
+* @param {PositiveNumber} lambda - shape parameter
+* @returns {number} evaluated MGF
+*
+* @example
+* var y = mgf( 0.2, 0.5 );
+* // returns ~1.5181
+*
+* @example
+* var y = mgf( 0.4, 1.5 );
+* // returns ~1.1645
+*
+* @example
+* var y = mgf( NaN, 0.0 );
+* // returns NaN
+*
+* @example
+* var y = mgf( 0.0, NaN );
+* // returns NaN
+*
+* @example
+* var y = mgf( 2.0, -1.0 );
+* // returns NaN
+*/
+function mgf( t, lambda ) {
+ if ( isnan( t ) || isnan( lambda ) || lambda <= 0.0 ) {
+ return NaN;
+ }
+ return expm1( -lambda ) / expm1( t - lambda );
+}
+
+
+// EXPORTS //
+
+module.exports = mgf;
diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/package.json b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/package.json
new file mode 100644
index 000000000000..4776d211666e
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/package.json
@@ -0,0 +1,67 @@
+{
+ "name": "@stdlib/stats/base/dists/planck/mgf",
+ "version": "0.0.0",
+ "description": "Planck (discrete exponential) distribution moment-generating function (MGF).",
+ "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",
+ "distribution",
+ "dist",
+ "mgf",
+ "generating functions",
+ "moments",
+ "memoryless",
+ "life-time",
+ "discrete",
+ "planck",
+ "univariate"
+ ]
+}
diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/test/fixtures/python/large_lambda.json b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/test/fixtures/python/large_lambda.json
new file mode 100644
index 000000000000..78c4a38595ee
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/test/fixtures/python/large_lambda.json
@@ -0,0 +1 @@
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diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/test/fixtures/python/runner.py b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/test/fixtures/python/runner.py
new file mode 100644
index 000000000000..019716218341
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/test/fixtures/python/runner.py
@@ -0,0 +1,86 @@
+#!/usr/bin/env python
+#
+# @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.
+
+"""Generate fixtures."""
+
+import os
+import json
+import numpy as np
+
+# Get the file path:
+FILE = os.path.realpath(__file__)
+
+# Extract the directory in which this file resides:
+DIR = os.path.dirname(FILE)
+
+
+def gen(x, lam, name):
+ """
+ Generate fixture data and write to file.
+
+ # Arguments
+
+ * `x`: input values.
+ * `lam`: shape parameter.
+ * `name::str`: output filename.
+
+ # Examples
+
+ ```python
+ python> x = np.random.rand(1000) * 10.0
+ python> lam = np.random.rand(1000)
+ python> gen(x, lam, "data.json")
+ ```
+ """
+ # Compute MGF values:
+ z = np.array(np.expm1(-lam) / np.expm1(x - lam))
+
+ # Store data to be written to file as a dictionary:
+ data = {
+ "x": x.tolist(),
+ "lambda": lam.tolist(),
+ "expected": z.tolist()
+ }
+
+ # Based on the script directory, create an output filepath:
+ filepath = os.path.join(DIR, name)
+
+ # Write the data to the output filepath as JSON:
+ with open(filepath, "w", encoding='utf-8') as outfile:
+ json.dump(data, outfile)
+
+ # Include trailing newline:
+ with open(filepath, "a", encoding='utf-8') as outfile:
+ outfile.write("\n")
+
+
+def main():
+ """Generate fixture data."""
+ # Large shape parameter:
+ x = np.round(np.random.rand(1000) * 10.0)
+ lam = (np.random.rand(1000) * 10.0) + 10.0
+ gen(x, lam, "large_lambda.json")
+
+ # Small shape parameter:
+ x = np.round(np.random.rand(1000) * 10.0)
+ lam = np.random.rand(1000) * 0.5
+ gen(x, lam, "small_lambda.json")
+
+
+if __name__ == "__main__":
+ main()
diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/test/fixtures/python/small_lambda.json b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/test/fixtures/python/small_lambda.json
new file mode 100644
index 000000000000..546ffd9d31c6
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/test/fixtures/python/small_lambda.json
@@ -0,0 +1 @@
+{"x": [6.0, 2.0, 1.0, 7.0, 7.0, 8.0, 9.0, 2.0, 0.0, 6.0, 1.0, 8.0, 5.0, 2.0, 5.0, 1.0, 5.0, 10.0, 2.0, 3.0, 9.0, 2.0, 2.0, 0.0, 9.0, 8.0, 3.0, 9.0, 3.0, 3.0, 2.0, 2.0, 0.0, 4.0, 4.0, 4.0, 8.0, 2.0, 2.0, 6.0, 6.0, 5.0, 1.0, 5.0, 6.0, 6.0, 5.0, 8.0, 8.0, 1.0, 10.0, 1.0, 2.0, 2.0, 4.0, 5.0, 5.0, 4.0, 5.0, 7.0, 6.0, 3.0, 8.0, 0.0, 4.0, 7.0, 5.0, 6.0, 5.0, 3.0, 4.0, 2.0, 1.0, 1.0, 6.0, 0.0, 4.0, 2.0, 9.0, 5.0, 4.0, 6.0, 4.0, 9.0, 8.0, 5.0, 6.0, 3.0, 5.0, 1.0, 5.0, 5.0, 1.0, 7.0, 8.0, 2.0, 9.0, 6.0, 9.0, 8.0, 3.0, 3.0, 1.0, 8.0, 1.0, 6.0, 2.0, 8.0, 2.0, 1.0, 4.0, 1.0, 4.0, 4.0, 1.0, 3.0, 4.0, 4.0, 3.0, 7.0, 4.0, 8.0, 9.0, 10.0, 0.0, 8.0, 4.0, 5.0, 9.0, 5.0, 2.0, 3.0, 7.0, 4.0, 1.0, 0.0, 5.0, 4.0, 7.0, 6.0, 9.0, 5.0, 3.0, 9.0, 9.0, 4.0, 7.0, 10.0, 2.0, 5.0, 8.0, 6.0, 4.0, 6.0, 1.0, 8.0, 4.0, 2.0, 4.0, 1.0, 9.0, 2.0, 2.0, 8.0, 8.0, 0.0, 7.0, 9.0, 5.0, 5.0, 3.0, 3.0, 1.0, 1.0, 8.0, 6.0, 8.0, 6.0, 6.0, 5.0, 4.0, 1.0, 9.0, 2.0, 2.0, 6.0, 0.0, 2.0, 2.0, 8.0, 8.0, 2.0, 0.0, 9.0, 6.0, 4.0, 8.0, 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/test/test.factory.js b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/test/test.factory.js
new file mode 100644
index 000000000000..ba3ecad8e09e
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/test/test.factory.js
@@ -0,0 +1,136 @@
+/**
+* @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 tape = require( 'tape' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var abs = require( '@stdlib/math/base/special/abs' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+var factory = require( './../lib/factory.js' );
+
+
+// FIXTURES //
+
+var smallLambda = require( './fixtures/python/small_lambda.json' );
+var largeLambda = require( './fixtures/python/large_lambda.json' );
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+ t.ok( true, __filename );
+ t.strictEqual( typeof factory, 'function', 'main export is a function' );
+ t.end();
+});
+
+tape( 'the function returns a function', function test( t ) {
+ var mgf = factory( 0.5 );
+ t.equal( typeof mgf, 'function', 'returns a function' );
+ t.end();
+});
+
+tape( 'if provided `NaN` for any parameter, the returned function returns `NaN`', function test( t ) {
+ var mgf;
+ var y;
+
+ mgf = factory( 0.5 );
+ y = mgf( NaN );
+ t.equal( isnan( y ), true, 'returns expected value' );
+
+ mgf = factory( NaN );
+ y = mgf( 0.0 );
+ t.equal( isnan( y ), true, 'returns expected value' );
+
+ t.end();
+});
+
+tape( 'if provided a shape parameter `lambda` which is nonpositive, the returned function always returns `NaN`', function test( t ) {
+ var mgf;
+ var y;
+
+ mgf = factory( 0.0 );
+ y = mgf( 2.0 );
+ t.equal( isnan( y ), true, 'returns expected value' );
+ y = mgf( 0.0 );
+ t.equal( isnan( y ), true, 'returns expected value' );
+
+ mgf = factory( -1.0 );
+ y = mgf( 2.0 );
+ t.equal( isnan( y ), true, 'returns expected value' );
+ y = mgf( 0.0 );
+ t.equal( isnan( y ), true, 'returns expected value' );
+
+ t.end();
+});
+
+tape( 'the returned function evaluates the mgf for `x` given small parameter `lambda`', function test( t ) {
+ var expected;
+ var lambda;
+ var delta;
+ var mgf;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ expected = smallLambda.expected;
+ x = smallLambda.x;
+ lambda = smallLambda.lambda;
+ for ( i = 0; i < x.length; i++ ) {
+ mgf = factory( lambda[ i ] );
+ y = mgf( x[ i ] );
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: '+x[ i ]+', lambda: '+lambda[ i ]+', y: '+y+', expected: '+expected[ i ] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 2.0 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: '+x[ i ]+'. lambda: '+lambda[ i ]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the returned function evaluates the mgf for `x` given large parameter `lambda`', function test( t ) {
+ var expected;
+ var lambda;
+ var delta;
+ var mgf;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ expected = largeLambda.expected;
+ x = largeLambda.x;
+ lambda = largeLambda.lambda;
+ for ( i = 0; i < x.length; i++ ) {
+ mgf = factory( lambda[ i ] );
+ y = mgf( x[ i ] );
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: '+x[ i ]+', lambda: '+lambda[ i ]+', y: '+y+', expected: '+expected[ i ] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 2.0 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: '+x[ i ]+'. lambda: '+lambda[ i ]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' );
+ }
+ }
+ t.end();
+});
diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/test/test.js b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/test/test.js
new file mode 100644
index 000000000000..9b8d315bdad7
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/test/test.js
@@ -0,0 +1,38 @@
+/**
+* @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 tape = require( 'tape' );
+var mgf = require( './../lib' );
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+ t.ok( true, __filename );
+ t.strictEqual( typeof mgf, 'function', 'main export is a function' );
+ t.end();
+});
+
+tape( 'attached to the main export is a factory method for generating `mgf` functions', function test( t ) {
+ t.equal( typeof mgf.factory, 'function', 'exports a factory method' );
+ t.end();
+});
diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/test/test.mgf.js b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/test/test.mgf.js
new file mode 100644
index 000000000000..7869c11968a8
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/planck/mgf/test/test.mgf.js
@@ -0,0 +1,112 @@
+/**
+* @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 tape = require( 'tape' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var abs = require( '@stdlib/math/base/special/abs' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+var mgf = require( './../lib' );
+
+
+// FIXTURES //
+
+var smallLambda = require( './fixtures/python/small_lambda.json' );
+var largeLambda = require( './fixtures/python/large_lambda.json' );
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+ t.ok( true, __filename );
+ t.strictEqual( typeof mgf, 'function', 'main export is a function' );
+ t.end();
+});
+
+tape( 'if provided `NaN` for any parameter, the function returns `NaN`', function test( t ) {
+ var y = mgf( NaN, 0.5 );
+ t.equal( isnan( y ), true, 'returns expected value' );
+ y = mgf( 4.0, NaN );
+ t.equal( isnan( y ), true, 'returns expected value' );
+ t.end();
+});
+
+tape( 'if provided a shape parameter `lambda` which is nonpositive, the function returns `NaN`', function test( t ) {
+ var y;
+
+ y = mgf( 3.0, 0.0 );
+ t.equal( isnan( y ), true, 'returns expected value' );
+
+ y = mgf( 3.0, -0.5 );
+ t.equal( isnan( y ), true, 'returns expected value' );
+
+ t.end();
+});
+
+tape( 'the function evaluates the mgf for `x` given small parameter `lambda`', function test( t ) {
+ var expected;
+ var lambda;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ expected = smallLambda.expected;
+ x = smallLambda.x;
+ lambda = smallLambda.lambda;
+ for ( i = 0; i < x.length; i++ ) {
+ y = mgf( x[ i ], lambda[ i ] );
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: '+x[ i ]+', lambda: '+lambda[ i ]+', y: '+y+', expected: '+expected[ i ] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 2.0 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: '+x[ i ]+'. lambda: '+lambda[ i ]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function evaluates the mgf for `x` given large parameter `lambda`', function test( t ) {
+ var expected;
+ var lambda;
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var i;
+
+ expected = largeLambda.expected;
+ x = largeLambda.x;
+ lambda = largeLambda.lambda;
+ for ( i = 0; i < x.length; i++ ) {
+ y = mgf( x[ i ], lambda[ i ] );
+ if ( y === expected[ i ] ) {
+ t.equal( y, expected[ i ], 'x: '+x[ i ]+', lambda: '+lambda[ i ]+', y: '+y+', expected: '+expected[ i ] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 2.0 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: '+x[ i ]+'. lambda: '+lambda[ i ]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' );
+ }
+ }
+ t.end();
+});