feat: add stats/base/dists/bradford/pdf

lib/node_modules/@stdlib/stats/base/dists/bradford/pdf/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.
+
+-->
+
+# Probability Density Function
+
+> [Bradford][bradford-distribution] distribution [probability density function][pdf] (PDF).
+
+<section class="intro">
+
+The [probability density function][pdf] (PDF) for a [bradford][bradford-distribution] random variable is
+
+<!-- <equation class="equation" label="eq:bradford_pdf" align="center" raw="f(x;c)=\frac{c}{(\ln(1+c)) (1 + cx)}" alt="Probability density function (PDF) for a bradford distribution."> -->
+
+```math
+f(x;c)=\frac{c}{(\ln(1+c)) (1 + cx)}
+```
+
+<!-- <div class="equation" align="center" data-raw-text="f(x;c)=\frac{c}{(\ln(1+c)) (1 + cx)}" data-equation="eq:bradford_pdf">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/bradford/pdf/docs/img/equation_bradford_pdf.svg" alt="Probability density function (PDF) for a bradford distribution.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+where `c` is the shape parameter of the distribution. The parameters must satisfy `0 <= x <= 1` and `c > 0`.
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var pdf = require( '@stdlib/stats/base/dists/bradford/pdf' );
+```
+
+#### pdf( x, c )
+
+Evaluates the [probability density function][pdf] (PDF) for a [bradford][bradford-distribution] distribution with shape parameter `c` at a value `x`.
+
+```javascript
+var y = pdf( 0.1, 0.1 );
+// returns ~1.039
+
+y = pdf( 0.5, 5.0 );
+// returns ~0.797
+
+y = pdf( 1.0, 10.0 );
+// returns ~0.379
+```
+
+If provided `NaN` as any argument, the function returns `NaN`.
+
+```javascript
+var y = pdf( NaN, 1.0 );
+// returns NaN
+
+y = pdf( 0.0, NaN );
+// returns NaN
+```
+
+If provided an input value `x` outside of the interval `[0,1]`, the function returns `NaN`.
+
+```javascript
+var y = pdf( 2.0, 1.0 );
+// returns NaN
+
+y = pdf( -0.5, 1.0 );
+// returns NaN
+```
+
+If provided a shape parameter `c <= 0`, the function returns `NaN`.
+
+```javascript
+var y = pdf( 0.0, 0.0 );
+// returns NaN
+
+y = pdf( 0.5, -1.0 );
+// returns NaN
+```
+
+#### pdf.factory( c )
+
+Returns a `function` for evaluating the [PDF][pdf] of a [bradford][bradford-distribution] distribution with shape parameter `c`.
+
+```javascript
+var myPDF = pdf.factory( 5.0 );
+var y = myPDF( 0.5 );
+// returns ~0.797
+
+y = myPDF( 1.0 );
+// returns ~0.465
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var randu = require( '@stdlib/random/base/randu' );
+var pdf = require( '@stdlib/stats/base/dists/bradford/pdf' );
+
+var x;
+var c;
+var y;
+var i;
+
+for ( i = 0; i < 25; i++ ) {
+    x = randu();
+    c = ( randu()*10.0 );
+    y = pdf( x, c );
+    console.log( 'x: %d, c: %d, f(x;c): %d', x.toFixed( 4 ), c.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">
+
+[pdf]: https://en.wikipedia.org/wiki/Probability_density_function
+
+[bradford-distribution]: https://en.wikipedia.org/wiki/Bradford%27s_law
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/stats/base/dists/bradford/pdf/benchmark/benchmark.js

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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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var Float64Array = require( '@stdlib/array/float64' );
+var uniform = require( '@stdlib/random/base/uniform' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pkg = require( './../package.json' ).name;
+var pdf = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var len;
+	var x;
+	var c;
+	var y;
+	var i;
+
+	len = 100;
+	x = new Float64Array( len );
+	c = new Float64Array( len );
+	for ( i = 0; i < len; i++ ) {
+		x[ i ] = uniform( 0.0, 1.0 );
+		c[ i ] = uniform( EPS, 10.0 );
+	}
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = pdf( x[ i % len ], c[ 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();
+});

lib/node_modules/@stdlib/stats/base/dists/bradford/pdf/docs/repl.txt

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+
+{{alias}}( x, c )
+    Evaluates the probability density function (PDF) for a bradford distribution
+    with shape parameter `c` at a value `x`.
+
+    If provided `NaN` as any argument, the function returns `NaN`.
+
+    If `x < 0` or `x > 1`, the function returns `NaN`.
+
+    If provided `c <= 0`, the function returns `NaN`.
+
+    Parameters
+    ----------
+    x: number
+        Input value.
+
+    c: number
+        Shape parameter.
+
+    Returns
+    -------
+    out: number
+        Evaluated PDF.
+
+    Examples
+    --------
+    > var y = {{alias}}( 0.1, 0.1 )
+    ~1.039
+    > y = {{alias}}( 0.5, 5.0 )
+    ~0.797
+    > y = {{alias}}( 1.0, 10.0 )
+    ~0.379
+    > y = {{alias}}( 0.5, 0.0 )
+    NaN
+    > y = {{alias}}( 2.0, 0.5 )
+    NaN
+    > y = {{alias}}( -1.0, 0.5 )
+    NaN
+    > y = {{alias}}( NaN, 1.0 )
+    NaN
+    > y = {{alias}}( 1.0, NaN )
+    NaN
+
+
+{{alias}}.factory( c )
+    Returns a function for evaluating the probability density function (PDF) of
+    a bradford distribution with shape parameter `c`.
+
+    Parameters
+    ----------
+    c: number
+        Shape parameter.
+
+    Returns
+    -------
+    pdf: Function
+        Probability density function (PDF).
+
+    Examples
+    --------
+    > var myPDF = {{alias}}.factory( 5.0 );
+    > var y = myPDF( 0.5 )
+    ~0.797
+    > y = myPDF( 1.0 )
+    ~0.465
+
+    See Also
+    --------
+