feat: add Wald distribution mgf package

lib/node_modules/@stdlib/stats/base/dists/wald/mgf/README.md

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+<!--
+
+@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.
+
+-->
+
+# Moment-Generating Function
+
+> [Wald][wald-distribution] distribution moment-generating function (MGF).
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
+
+<section class="intro">
+
+The [moment-generating function][mgf] for a [Wald][wald-distribution] random variable is
+
+<!-- <equation class="equation" label="eq:wald_mgf_function" align="center" raw="M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = \exp\left[\frac{\lambda}{\mu}\left(1-\sqrt{1-\frac{2\mu^2 t}{\lambda}}\right)\right]" alt="Moment-generating function (MGF) for a Wald distribution."> -->
+
+```math
+M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = \exp\left[\frac{\lambda}{\mu}\left(1-\sqrt{1-\frac{2\mu^2 t}{\lambda}}\right)\right]
+```
+
+<!-- <div class="equation" align="center" data-raw-text="M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = \exp\left[\frac{\lambda}{\mu}\left(1-\sqrt{1-\frac{2\mu^2 t}{\lambda}}\right)\right]" data-equation="eq:wald_mgf_function">
+    <img src="" alt="Moment-generating function (MGF) for a Wald distribution.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+where `mu > 0` is the mean and `lambda > 0` is the shape parameter. The MGF is defined for `t < lambda / (2 * mu^2)`.
+
+</section>
+
+<!-- /.intro -->
+
+<!-- Package usage documentation. -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var mgf = require( '@stdlib/stats/base/dists/wald/mgf' );
+```
+
+#### mgf( t, mu, lambda )
+
+Evaluates the [moment-generating function][mgf] (MGF) for a [Wald][wald-distribution] distribution with parameters `mu` (mean) and `lambda` (shape parameter).
+
+```javascript
+var y = mgf( 0.1, 2.0, 3.0 );
+// returns ~1.2405
+
+y = mgf( -1.0, 0.5, 2.0 );
+// returns ~0.6237
+```
+
+If provided `NaN` as any argument, the function returns `NaN`.
+
+```javascript
+var y = mgf( NaN, 0.5, 2.0 );
+// returns NaN
+
+y = mgf( 0.1, NaN, 2.0 );
+// returns NaN
+
+y = mgf( 0.1, 0.5, NaN );
+// returns NaN
+```
+
+If provided `mu <= 0`, the function returns `NaN`.
+
+```javascript
+var y = mgf( 0.1, -1.0, 2.0 );
+// returns NaN
+```
+
+If provided `lambda <= 0`, the function returns `NaN`.
+
+```javascript
+var y = mgf( 0.1, 0.5, -2.0 );
+// returns NaN
+```
+
+If provided `t >= lambda / (2 * mu^2)`, the function returns `NaN`.
+
+```javascript
+var y = mgf( 1.0, 2.0, 3.0 );
+// returns NaN
+```
+
+#### mgf.factory( mu, lambda )
+
+Returns a function for evaluating the [moment-generating function][mgf] (MGF) of a [Wald][wald-distribution] distribution with parameters `mu` and `lambda`.
+
+```javascript
+var mymgf = mgf.factory( 2.0, 3.0 );
+
+var y = mymgf( 0.1 );
+// returns ~1.2405
+
+y = mymgf( 0.2 );
+// returns ~1.6085
+```
+
+</section>
+
+<!-- /.usage -->
+
+<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<!-- Package usage examples. -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var uniform = require( '@stdlib/random/array/uniform' );
+var logEachMap = require( '@stdlib/console/log-each-map' );
+var mgf = require( '@stdlib/stats/base/dists/wald/mgf' );
+
+var opts = {
+    'dtype': 'float64'
+};
+var lambda = uniform( 10, 50.0, 100.0, opts );
+var mu = uniform( 10, 0.1, 2.0, opts );
+var t = uniform( 10, -5.0, 5.0, opts );
+
+logEachMap( 't: %0.4f, µ: %0.4f, λ: %0.4f, M_X(t;µ,λ): %0.4f', t, mu, lambda, mgf );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- C interface documentation. -->
+
+* * *
+
+<section class="c">
+
+## C APIs
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<!-- C usage documentation. -->
+
+<section class="usage">
+
+### Usage
+
+```c
+#include "stdlib/stats/base/dists/wald/mgf.h"
+```
+
+#### stdlib_base_dists_wald_mgf( t, mu, lambda )
+
+Evaluates the [moment-generating function][mgf] (MGF) for a [Wald][wald-distribution] distribution with parameters `mu` (mean) and `lambda` (shape parameter).
+
+```c
+double y = stdlib_base_dists_wald_mgf( 0.1, 2.0, 3.0 );
+// returns ~1.2405
+```
+
+The function accepts the following arguments:
+
+-   **t**: `[in] double` input value.
+-   **mu**: `[in] double` mean.
+-   **lambda**: `[in] double` shape parameter.
+
+```c
+double stdlib_base_dists_wald_mgf( const double t, const double mu, const double lambda );
+```
+
+</section>
+
+<!-- /.usage -->
+
+<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<!-- C API usage examples. -->
+
+<section class="examples">
+
+### Examples
+
+```c
+#include "stdlib/stats/base/dists/wald/mgf.h"
+#include <stdlib.h>
+#include <stdio.h>
+
+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 lambda;
+    double mu;
+    double t;
+    double y;
+    int i;
+
+    for ( i = 0; i < 10; i++ ) {
+        t = random_uniform( -5.0, 5.0 );
+        mu = random_uniform( 0.1, 2.0 );
+        lambda = random_uniform( 50.0, 100.0 );
+        y = stdlib_base_dists_wald_mgf( t, mu, lambda );
+        printf( "t: %lf, µ: %lf, λ: %lf, M_X(t;µ,λ): %lf\n", t, mu, lambda, y );
+    }
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
+<!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="references">
+
+</section>
+
+<!-- /.references -->
+
+<!-- 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">
+
+[wald-distribution]: https://en.wikipedia.org/wiki/Inverse_Gaussian_distribution
+
+[mgf]: https://en.wikipedia.org/wiki/Moment-generating_function
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/stats/base/dists/wald/mgf/benchmark/benchmark.js

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+/**
+* @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 format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var mgf = require( './../lib' );
+
+
+// MAIN //
+
+bench(pkg, function benchmark(b) {
+	var lambda;
+	var opts;
+	var mu;
+	var t;
+	var y;
+	var i;
+
+	opts = {
+		'dtype': 'float64'
+	};
+	t = uniform(100, -5.0, 5.0, opts);
+	mu = uniform(100, 0.1, 2.0, opts);
+	lambda = uniform(100, 50.0, 100.0, opts);
+
+	b.tic();
+	for (i = 0; i < b.iterations; i++) {
+		y = mgf( t[ i%t.length ], mu[ i%mu.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(format('%s:factory', pkg), function benchmark(b) {
+	var mymgf;
+	var t;
+	var y;
+	var i;
+
+	mymgf = mgf.factory(2.0, 50.0);
+	t = uniform(100, -5.0, 5.0, {
+		'dtype': 'float64'
+	});
+
+	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();
+});