feat: Added Rice Distribution Base Package

Author: CodeMaverick2

lib/node_modules/@stdlib/stats/base/dists/rice/Readme.md

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+# Rice Distribution
+
+This package implements the Rice distribution for the `@stdlib` library.
+
+## Overview
+
+The Rice distribution is a continuous probability distribution. This package provides the following primary functions:
+
+- **PDF (Probability Density Function)**
+- **CDF (Cumulative Distribution Function)**
+
+## Installation
+
+```bash
+npm install @stdlib/stats-base-dists-rice
+```
+
+## Usage
+
+### PDF
+
+The PDF function evaluates the probability density function for given `x`, `nu`, and `sigma`.
+
+#### Syntax
+
+```javascript
+var pdf = require('@stdlib/stats/base/dists/rice/pdf');
+
+pdf(x, nu, sigma);
+```
+
+#### Example
+
+```javascript
+var pdf = require('@stdlib/stats/base/dists/rice/pdf');
+
+var y = pdf(2, 1, 1);
+console.log(y);  // returns the PDF value at x=2 for nu=1 and sigma=1
+```
+
+### CDF
+
+The CDF function evaluates the cumulative distribution function for given `x`, `nu`, and `sigma`.
+
+#### Syntax
+
+```javascript
+var cdf = require('@stdlib/stats/base/dists/rice/cdf');
+
+cdf(x, nu, sigma);
+```
+
+#### Example
+
+```javascript
+var cdf = require('@stdlib/stats/base/dists/rice/cdf');
+
+var y = cdf(2, 1, 1);
+console.log(y);  // returns the CDF value at x=2 for nu=1 and sigma=1
+```
+
+## Testing
+
+To run the tests, use the following commands:
+
+```bash
+npm install
+npm test
+```
+
+
+

lib/node_modules/@stdlib/stats/base/dists/rice/lib/cdf.js

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+'use strict';
+
+/**
+ * Evaluates the cumulative distribution function (CDF) for a Rice distribution.
+ *
+ * @param {number} x - input value
+ * @param {number} nu - noncentrality parameter
+ * @param {number} sigma - scale parameter
+ * @returns {number} evaluated CDF
+ */
+function cdf(x, nu, sigma) {
+    if (sigma <= 0) {
+        throw new Error('Scale parameter `sigma` must be positive');
+    }
+    const z = x / sigma;
+    const bessel = require('@stdlib/math/base/special/besseli');
+    const normal = require('@stdlib/stats/base/dists/normal/cdf');
+    return normal.cdf(z, nu / sigma, 1) - Math.exp(-z * z / 2 - nu * nu / (2 * sigma * sigma)) * bessel(z * nu / sigma, 1);
+}
+
+module.exports = cdf;

lib/node_modules/@stdlib/stats/base/dists/rice/lib/index.js

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+'use strict';
+
+var pdf = require('./pdf');
+var cdf = require('./cdf');
+
+module.exports = {
+    pdf: pdf,
+    cdf: cdf
+};

lib/node_modules/@stdlib/stats/base/dists/rice/lib/pdf.js

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+'use strict';
+
+/**
+ * Evaluates the probability density function (PDF) for a Rice distribution.
+ *
+ * @param {number} x - input value
+ * @param {number} nu - noncentrality parameter
+ * @param {number} sigma - scale parameter
+ * @returns {number} evaluated PDF
+ */
+function pdf(x, nu, sigma) {
+    if (sigma <= 0) {
+        throw new Error('Scale parameter `sigma` must be positive');
+    }
+    const factor = x / (sigma * sigma);
+    const expFactor = Math.exp(-((x*x + nu*nu) / (2 * sigma * sigma)));
+    const bessel = require('@stdlib/math/base/special/bessel0');
+    return factor * expFactor * bessel(x * nu / (sigma * sigma));
+}
+
+module.exports = pdf;

lib/node_modules/@stdlib/stats/base/dists/rice/test/test.cdf.js

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+'use strict';
+
+var tape = require('tape');
+var cdf = require('./../lib/cdf');
+
+tape('CDF of Rice distribution', function (t) {
+    t.equal(cdf(2, 1, 1), /* expected value */);
+    t.end();
+});

lib/node_modules/@stdlib/stats/base/dists/rice/test/test.js

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+'use strict';
+
+var tape = require('tape');
+var rice = require('./../lib');
+
+tape('main export is an object', function (t) {
+    t.equal(typeof rice, 'object', 'main export is an object');
+    t.end();
+});

lib/node_modules/@stdlib/stats/base/dists/rice/test/test.pdf.js

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+'use strict';
+
+var tape = require('tape');
+var pdf = require('./../lib/pdf');
+
+tape('PDF of Rice distribution', function (t) {
+    t.equal(pdf(2, 1, 1), /* expected value */);
+    t.end();
+});