feat(wald/ctor): wald ctor benchmarks, docs, examples, lib, tests

lib/node_modules/@stdlib/stats/base/dists/wald/ctor/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.
+
+-->
+
+# Wald
+
+> Wald distribution constructor.
+
+<!-- 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 -->
+
+<!-- Package usage documentation. -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var Wald = require( '@stdlib/stats/base/dists/wald/ctor' );
+```
+
+#### Wald( \[mu, lambda] )
+
+Returns a [Wald][wald-distribution] (inverse Gaussian) distribution object.
+
+```javascript
+var wald = new Wald();
+
+var mu = wald.mean;
+// returns 1.0
+```
+
+By default, `mu = 1.0` and `lambda = 1.0`. To create a distribution having a different `mu` (mean parameter) and `lambda` (shape parameter), provide the corresponding arguments.
+
+```javascript
+var wald = new Wald( 2.0, 4.0 );
+
+var mu = wald.mean;
+// returns 2.0
+```
+
+* * *
+
+## wald
+
+A [Wald][wald-distribution] distribution object has the following properties and methods...
+
+### Writable Properties
+
+#### wald.mu
+
+Mean parameter of the distribution. `mu` **must** be a positive number.
+
+```javascript
+var wald = new Wald();
+
+var mu = wald.mu;
+// returns 1.0
+
+wald.mu = 3.0;
+
+mu = wald.mu;
+// returns 3.0
+```
+
+#### wald.lambda
+
+Shape parameter of the distribution. `lambda` **must** be a positive number.
+
+```javascript
+var wald = new Wald( 2.0, 4.0 );
+
+var lambda = wald.lambda;
+// returns 4.0
+
+wald.lambda = 3.0;
+
+lambda = wald.lambda;
+// returns 3.0
+```
+
+* * *
+
+### Computed Properties
+
+#### Wald.prototype.kurtosis
+
+Returns the [excess kurtosis][kurtosis].
+
+```javascript
+var wald = new Wald( 4.0, 12.0 );
+
+var kurtosis = wald.kurtosis;
+// returns 5.0
+```
+
+#### Wald.prototype.mean
+
+Returns the [expected value][expected-value].
+
+```javascript
+var wald = new Wald( 4.0, 12.0 );
+
+var mu = wald.mean;
+// returns 4.0
+```
+
+#### Wald.prototype.mode
+
+Returns the [mode][mode].
+
+```javascript
+var wald = new Wald( 4.0, 12.0 );
+
+var mode = wald.mode;
+// returns ~2.472
+```
+
+#### Wald.prototype.skewness
+
+Returns the [skewness][skewness].
+
+```javascript
+var wald = new Wald( 4.0, 12.0 );
+
+var skewness = wald.skewness;
+// returns ~1.732
+```
+
+#### Wald.prototype.stdev
+
+Returns the [standard deviation][standard-deviation].
+
+```javascript
+var wald = new Wald( 4.0, 12.0 );
+
+var s = wald.stdev;
+// returns ~2.309
+```
+
+#### Wald.prototype.variance
+
+Returns the [variance][variance].
+
+```javascript
+var wald = new Wald( 4.0, 12.0 );
+
+var s2 = wald.variance;
+// returns ~5.333
+```
+
+* * *
+
+### Methods
+
+#### Wald.prototype.cdf( x )
+
+Evaluates the [cumulative distribution function][cdf] (CDF).
+
+```javascript
+var wald = new Wald( 2.0, 4.0 );
+
+var y = wald.cdf( 0.5 );
+// returns ~0.028
+```
+
+#### Wald.prototype.logcdf( x )
+
+Evaluates the natural logarithm of the [cumulative distribution function][cdf] (CDF).
+
+```javascript
+var wald = new Wald( 2.0, 4.0 );
+
+var y = wald.logcdf( 0.5 );
+// returns ~-3.574
+```
+
+#### Wald.prototype.logpdf( x )
+
+Evaluates the natural logarithm of the [probability density function][pdf] (PDF).
+
+```javascript
+var wald = new Wald( 2.0, 4.0 );
+
+var y = wald.logpdf( 0.8 );
+// returns ~-0.791
+```
+
+#### Wald.prototype.mgf( t )
+
+Evaluates the [moment-generating function][mgf] (MGF).
+
+```javascript
+var wald = new Wald( 2.0, 4.0 );
+
+var y = wald.mgf( 0.01 );
+// returns ~1.02
+```
+
+#### Wald.prototype.pdf( x )
+
+Evaluates the [probability density function][pdf] (PDF).
+
+```javascript
+var wald = new Wald( 2.0, 4.0 );
+
+var y = wald.pdf( 0.8 );
+// returns ~0.453
+```
+
+#### Wald.prototype.quantile( p )
+
+Evaluates the [quantile function][quantile-function] at probability `p`.
+
+```javascript
+var wald = new Wald( 2.0, 4.0 );
+
+var y = wald.quantile( 0.5 );
+// returns ~1.609
+
+y = wald.quantile( 1.9 );
+// returns NaN
+```
+
+</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 Wald = require( '@stdlib/stats/base/dists/wald/ctor' );
+
+var wald = new Wald( 2.0, 4.0 );
+
+var mean = wald.mean;
+// returns 2.0
+
+var s2 = wald.variance;
+// returns 2.0
+
+var y = wald.cdf( 0.8 );
+// returns ~0.137
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- 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
+
+[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
+
+[mgf]: https://en.wikipedia.org/wiki/Moment-generating_function
+
+[pdf]: https://en.wikipedia.org/wiki/Probability_density_function
+
+[quantile-function]: https://en.wikipedia.org/wiki/Quantile_function
+
+[expected-value]: https://en.wikipedia.org/wiki/Expected_value
+
+[kurtosis]: https://en.wikipedia.org/wiki/Kurtosis
+
+[mode]: https://en.wikipedia.org/wiki/Mode_%28statistics%29
+
+[skewness]: https://en.wikipedia.org/wiki/Skewness
+
+[standard-deviation]: https://en.wikipedia.org/wiki/Standard_deviation
+
+[variance]: https://en.wikipedia.org/wiki/Variance
+
+</section>
+
+<!-- /.links -->