stdlib-js · vivekmaurya001 · Mar 9, 2025 · Mar 9, 2025 · Mar 16, 2025 · Mar 16, 2025
diff --git a/lib/node_modules/@stdlib/stats/base/dists/burr-type3/cdf/README.md b/lib/node_modules/@stdlib/stats/base/dists/burr-type3/cdf/README.md
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+<!--
+
+@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.
+
+-->
+
+# 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; alpha, beta) = (1 + x^{-alpha})^{-beta}
+```
+
+<!-- <div class="equation" align="center" data-raw-text="F(x;c,d) = (1 + x^{-c})^{-d}" data-equation="eq:burr-type3_cdf">
+    <img src="https://quicklatex.com/cache3/1e/ql_96e6c56a3c01ce5db3f378b28ee9511e_l3.png" alt="Cumulative distribution function for a Burr (Type III) distribution.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+where `alpha > 0` is the first shape parameter and `beta > 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, alpha, beta )
+
+Evaluates the [cumulative distribution function][cdf] (CDF) for a [Burr (type III)][burr-distribution] distribution with parameters `alpha` (first shape parameter) and `beta` (second shape parameter).
+
+```javascript
+var y = cdf( 0.1, 1.0, 1.0 );
+// returns ~0.09
+
+y = cdf( 0.2, 2.0, 2.0 );
+// returns ~0.0015
+
+y = cdf( 0.4, 4.0, 4.0 );
+// returns ~3.88e-7
+
+y = cdf( 1.0, 0.1, 1.0 );
+// returns 0.5
+
+y = cdf( 0.3, 0.5, 0.5 );
+// returns ~0.59
+
+y = cdf( 0.5, 1.0, 1.0 );
+// returns ~0.33
+
+y = cdf( 0.5, 2.0, 4.0 );
+// returns ~0.0016
+
+y = cdf( 0.8, 0.5, 0.5 );
+// returns ~0.69
+```
+
+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 `alpha <= 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 `beta <= 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( alpha, beta )
+
+Returns a function for evaluating the [cumulative distribution function][cdf] for a [Burr (type III)][burr-distribution] distribution with parameters `alpha` (first shape parameter) and `beta` (second shape parameter).
+
+```javascript
+var mycdf = cdf.factory( 0.5, 0.5 );
+
+var y = mycdf( 0.8 );
+// returns ~0.69
+
+y = mycdf( 0.3 );
+// returns ~0.59
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var cdf = require( '@stdlib/stats/base/dists/burr-type3/cdf' );
+var linspace = require( '@stdlib/array/linspace' );
+
+var alpha = linspace( 1, 10.0, 10 );
+var beta = linspace( 1, 10.0, 10 );
+var x = linspace( 0.1, 1.0, 10 );
+var y;
+var i;
+
+for ( i = 0; i < 10; i++ ) {
+    y = cdf( x[ i ], alpha[ i ], beta[ i ] );
+    console.log( 'x: %d, α: %d, β: %d, F(x;α,β): %d', x[i].toFixed( 4 ), alpha[i].toFixed( 4 ), beta[i].toFixed( 4 ), y.toFixed( 4 ) );
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- 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 -->
diff --git a/lib/node_modules/@stdlib/stats/base/dists/burr-type3/cdf/benchmark/benchmark.js b/lib/node_modules/@stdlib/stats/base/dists/burr-type3/cdf/benchmark/benchmark.js
@@ -0,0 +1,84 @@
+/**
+* @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 cdf = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var alpha;
+	var beta;
+	var len;
+	var x;
+	var y;
+	var i;
+
+	len = 100;
+	x = uniform( len, 0.0, 10.0 );
+	alpha = uniform( len, 0.1, 100.0 );
+	beta = uniform( len, 0.1, 100.0 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = cdf( x[ i % len ], alpha[ i % len ], beta[ i % len ] );
+		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 mycdf;
+	var len;
+	var x;
+	var y;
+	var i;
+
+	len = 100;
+	x = uniform( len, 0.0, 10.0 );
+	mycdf = cdf.factory( 5.0, 6.0 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = mycdf( x[ i % len ] );
+		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/burr-type3/cdf/benchmark/python/benchmark.scipy.py b/lib/node_modules/@stdlib/stats/base/dists/burr-type3/cdf/benchmark/python/benchmark.scipy.py
@@ -0,0 +1,97 @@
+#!/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.
+
+"""Benchmark scipy.stats.burr.cdf."""
+
+from __future__ import print_function
+import timeit
+
+NAME = "burr:cdf"
+REPEATS = 3
+ITERATIONS = 1000
+
+
+def print_version():
+    """Print the TAP version."""
+    print("TAP version 13")
+
+
+def print_summary(total, passing):
+    """Print the benchmark summary.
+
+    # Arguments
+
+    * `total`: total number of tests
+    * `passing`: number of passing tests
+
+    """
+    print("#")
+    print("1.." + str(total))  # TAP plan
+    print("# total " + str(total))
+    print("# pass  " + str(passing))
+    print("#")
+    print("# ok")
+
+
+def print_results(elapsed):
+    """Print benchmark results.
+
+    # Arguments
+
+    * `elapsed`: elapsed time (in seconds)
+
+    # Examples
+
+    ``` python
+    python> print_results(0.131009101868)
+    ```
+    """
+    rate = ITERATIONS / elapsed
+
+    print("  ---")
+    print("  iterations: " + str(ITERATIONS))
+    print("  elapsed: " + str(elapsed))
+    print("  rate: " + str(rate))
+    print("  ...")
+
+
+def benchmark():
+    """Run the benchmark and print benchmark results."""
+    setup = "from scipy.stats import burr; from random import random;"
+    stmt = "y = burr.cdf(random(), 100.56789, 55.54321)"
+
+    t = timeit.Timer(stmt, setup=setup)
+
+    print_version()
+
+    for i in range(REPEATS):
+        print("# python::" + NAME)
+        elapsed = t.timeit(number=ITERATIONS)
+        print_results(elapsed)
+        print("ok " + str(i+1) + " benchmark finished")
+
+    print_summary(REPEATS, REPEATS)
+
+
+def main():
+    """Run the benchmark."""
+    benchmark()
+
+
+if __name__ == "__main__":
+    main()