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

lib/node_modules/@stdlib/stats/base/dists/bradford/variance/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.
+
+-->
+
+# Mean
+
+> [Bradford][bradford-distribution] distribution [variance][variance].
+
+<!-- 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">
+
+The [variance][variance] for a [Bradford][bradford-distribution] random variable is
+
+<!-- <equation class="equation" label="eq:bradford_variance" align="center" raw="\mathop{\mathrm{Var}}\left( X \right) = \frac{(c+2) \ln(1+c) - 2c}{2c (\ln(1+c))^2}" alt="Variance for a Bradford distribution."> -->
+
+```math
+\mathop{\mathrm{Var}}\left( X \right) = \frac{(c+2) \ln(1+c) - 2c}{2c (\ln(1+c))^2}
+```
+
+<!-- <div class="equation" align="center" data-raw-text="\mathop{\mathrm{Var}}\left( X \right) = \frac{(c+2) \ln(1+c) - 2c}{2c (\ln(1+c))^2}" data-equation="eq:bradford_variance">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/docs/img/equation_bradford_variance.svg" alt="Variance for a Bradford distribution.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+where `c` is the shape parameter.
+
+</section>
+
+<!-- /.intro -->
+
+<!-- Package usage documentation. -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var variance = require( '@stdlib/stats/base/dists/bradford/variance' );
+```
+
+#### variance( c )
+
+Returns the [variance][variance] of a [Bradford][bradford-distribution] distribution with shape parameter `c`.
+
+```javascript
+var v = variance( 0.1 );
+// returns ~0.083
+
+v = variance( 10.0 );
+// returns ~0.076
+```
+
+If provided a shape parameter `c <= 0`, the function returns `NaN`.
+
+```javascript
+var v = variance( 0.0 );
+// returns NaN
+
+v = variance( -1.5 );
+// 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 uniform = require( '@stdlib/random/array/uniform' );
+var variance = require( '@stdlib/stats/base/dists/bradford/variance' );
+
+var c = uniform( 10, 0.1, 10.0 );
+
+var v;
+var i;
+for ( i = 0; i < c.length; i++ ) {
+    v = variance( c[ i ] );
+    console.log( 'c: %d, Var(X;c): %d', c[ i ].toFixed( 4 ), v.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">
+
+[bradford-distribution]: https://en.wikipedia.org/wiki/Bradford%27s_law
+
+[variance]: https://en.wikipedia.org/wiki/Variance
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/stats/base/dists/bradford/variance/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 uniform = require( '@stdlib/random/array/uniform' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pkg = require( './../package.json' ).name;
+var variance = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var c;
+	var y;
+	var i;
+
+	c = uniform( 100, 0.1, 10.0 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = variance( c[ i % c.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();
+});

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

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+
+{{alias}}( c )
+    Returns the variance of a Bradford distribution with shape
+    parameter `c`.
+
+    If `c <= 0`, the function returns `NaN`.
+
+    Parameters
+    ----------
+    c: number
+        Shape parameter.
+
+    Returns
+    -------
+    out: number
+        Variance.
+
+    Examples
+    --------
+    > var v = {{alias}}( 0.1 )
+    ~0.083
+    > v = {{alias}}( 0.5 )
+    ~0.083
+    > v = {{alias}}( 10.0 )
+    ~0.076
+
+    See Also
+    --------
+

lib/node_modules/@stdlib/stats/base/dists/bradford/variance/docs/types/index.d.ts

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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.
+*/
+
+// TypeScript Version: 4.1
+
+/**
+* Returns the variance of a Bradford distribution.
+*
+* ## Notes
+*
+* -   If `c <= 0`, the function returns `NaN`.
+*
+* @param c - shape parameter
+* @returns variance
+*
+* @example
+* var v = variance( 0.1 );
+* // returns ~0.083
+*
+* @example
+* var v = variance( 0.5 );
+* // returns ~0.083
+*
+* @example
+* var v = variance( 10.0 );
+* // returns ~0.076
+*
+* @example
+* var v = variance( 0.0 );
+* // returns NaN
+*
+* @example
+* var v = variance( -1.0 );
+* // returns NaN
+*
+* @example
+* var v = variance( NaN );
+* // returns NaN
+*/
+declare function variance( c: number ): number;
+
+
+// EXPORTS //
+
+export = variance;