feat: add stats/base/dists/burr-type3/cdf

lib/node_modules/@stdlib/stats/base/dists/burr-type3/cdf/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.
+
+-->
+
+# Cumulative Distribution Function
+
+> [Burr (type III)][burr-distribution] distribution [cumulative distribution function][cdf].
+
+<section class="intro">
+
+The [cumulative distribution function][cdf] for a [Burr (type III)][burr-distribution] random variable is
+
+<!-- <equation class="equation" label="eq:burr_type3_cdf" align="center" raw="F(x; c, d) = (1 + x^{-c})^{-d}" alt="Cumulative distribution function for a Burr (Type III) distribution."> -->
+
+```math
+F(x; c, d) = (1 + x^{-c})^{-d}
+```
+
+<!-- </equation> -->
+
+where `c > 0` is the first shape parameter and `d > 0` is the second shape parameter.
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var cdf = require( '@stdlib/stats/base/dists/burr-type3/cdf' );
+```
+
+#### cdf( x, c, d )
+
+Evaluates the [cumulative distribution function][cdf] (CDF) for a [Burr (type III)][burr-distribution] distribution with parameters `c` (first shape parameter) and `d` (second shape parameter).
+
+```javascript
+var y = cdf( 0.1, 1.0, 1.0 );
+// returns ~0.091
+
+y = cdf( 0.2, 2.0, 2.0 );
+// returns ~0.0015
+
+y = cdf( 0.3, 2.0, 2.0 );
+// returns ~0.007
+
+y = cdf( 1.0, 0.1, 1.0 );
+// returns 0.5
+
+y = cdf( 0.3, 0.5, 0.5 );
+// returns ~0.595
+
+y = cdf( 0.5, 1.0, 1.0 );
+// returns ~0.333
+
+y = cdf( 0.5, 2.0, 4.0 );
+// returns ~0.0016
+
+y = cdf( 0.8, 0.5, 0.5 );
+// returns ~0.687
+```
+
+If provided `x <= 0`, the function returns `0`.
+
+```javascript
+var y = cdf( -1.0, 0.5, 1.0 );
+// returns 0.0
+
+y = cdf( 0.0, 0.5, 1.0 );
+// returns 0.0
+```
+
+If provided `NaN` as any argument, the function returns `NaN`.
+
+```javascript
+var y = cdf( NaN, 1.0, 1.0 );
+// returns NaN
+
+y = cdf( 0.0, NaN, 1.0 );
+// returns NaN
+
+y = cdf( 0.0, 1.0, NaN );
+// returns NaN
+```
+
+If provided `c <= 0`, the function returns `NaN`.
+
+```javascript
+var y = cdf( 2.0, -1.0, 0.5 );
+// returns NaN
+
+y = cdf( 2.0, 0.0, 0.5 );
+// returns NaN
+```
+
+If provided `d <= 0`, the function returns `NaN`.
+
+```javascript
+var y = cdf( 2.0, 0.5, -1.0 );
+// returns NaN
+
+y = cdf( 2.0, 0.5, 0.0 );
+// returns NaN
+```
+
+#### cdf.factory( c, d )
+
+Returns a function for evaluating the [cumulative distribution function][cdf] for a [Burr (type III)][burr-distribution] distribution with parameters `c` (first shape parameter) and `d` (second shape parameter).
+
+```javascript
+var mycdf = cdf.factory( 0.5, 0.5 );
+
+var y = mycdf( 0.8 );
+// returns ~0.687
+
+y = mycdf( 0.3 );
+// returns ~0.595
+```
+
+</section>
+
+<!-- /.usage -->
+
+<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 cdf = require( '@stdlib/stats/base/dists/burr-type3/cdf' );
+
+var opts = {
+    'dtype': 'float64'
+};
+var x = uniform( 10, 0.1, 1.0, opts );
+var c = uniform( 10, 1.0, 10.0, opts );
+var d = uniform( 10, 1.0, 10.0, opts );
+
+logEachMap( 'x: %0.4f, c: %0.4f, d: %0.4f, F(x;c,d): %0.4f', x, c, d, cdf );
+```
+
+</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/burr-type3/cdf.h"
+```
+
+#### stdlib_base_dists_burr_type3_cdf( x, c, d )
+
+Evaluates the cumulative distribution function (CDF) for a Burr (type III) distribution with first shape parameter `c` and second shape parameter `d` at input value `x`.
+
+```c
+double y = stdlib_base_dists_burr_type3_cdf( 0.1, 1.0, 1.0 );
+// returns ~0.091
+```
+
+The function accepts the following arguments:
+
+-   **x**: `[in] double` input value.
+-   **c**: `[in] double` first shape parameter.
+-   **d**: `[in] double` second shape parameter.
+
+```c
+double stdlib_base_dists_burr_type3_cdf( const double x, const double c, const double d );
+```
+
+</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/burr-type3/cdf.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 x;
+    double c;
+    double d;
+    double y;
+    int i;
+
+    for ( i = 0; i < 10; i++ ) {
+        x = random_uniform( 0.1, 1.0 );
+        c = random_uniform( 1.0, 10.0 );
+        d = random_uniform( 1.0, 10.0 );
+        y = stdlib_base_dists_burr_type3_cdf( x, c, d );
+        printf( "x: %lf, c: %lf, d: %lf, F(x;c,d): %lf\n", x, c, d, y );
+    }
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
+<!-- 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">
+
+[burr-distribution]: https://en.wikipedia.org/wiki/Burr_distribution
+
+[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/stats/base/dists/burr-type3/cdf/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 cdf = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var opts;
+	var c;
+	var d;
+	var x;
+	var y;
+	var i;
+
+	opts = {
+		'dtype': 'float64'
+	};
+	x = uniform( 100, 0.0, 10.0, opts );
+	c = uniform( 100, 0.1, 100.0, opts );
+	d = uniform( 100, 0.1, 100.0, opts );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = cdf( x[ i % x.length ], c[ i % c.length ], d[ i % d.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 mycdf;
+	var opts;
+	var x;
+	var y;
+	var i;
+
+	opts = {
+		'dtype': 'float64'
+	};
+	x = uniform( 100, 0.0, 10.0, opts );
+	mycdf = cdf.factory( 5.0, 6.0 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = mycdf( x[ i % x.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();
+});