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feat: add stats/base/dists/bradford/variance
PR-URL: #5326 Ref: #168 Reviewed-by: Philipp Burckhardt <[email protected]>
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Diff for: ‎lib/node_modules/@stdlib/stats/base/dists/bradford/variance/README.md

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<!--
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@license Apache-2.0
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Copyright (c) 2025 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# Variance
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> [Bradford][bradford-distribution] distribution [variance][variance].
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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The [variance][variance] for a [Bradford][bradford-distribution] random variable is
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<!-- <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."> -->
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```math
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\mathop{\mathrm{Var}}\left( X \right) = \frac{(c+2) \ln(1+c) - 2c}{2c (\ln(1+c))^2}
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```
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<!-- <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">
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<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.">
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<br>
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</div> -->
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<!-- </equation> -->
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where `c` is the shape parameter.
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</section>
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<!-- /.intro -->
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<!-- Package usage documentation. -->
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<section class="usage">
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## Usage
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```javascript
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var variance = require( '@stdlib/stats/base/dists/bradford/variance' );
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```
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#### variance( c )
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Returns the [variance][variance] of a [Bradford][bradford-distribution] distribution with shape parameter `c`.
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```javascript
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var v = variance( 0.1 );
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// returns ~0.083
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v = variance( 10.0 );
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// returns ~0.076
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```
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If provided a shape parameter `c <= 0`, the function returns `NaN`.
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```javascript
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var v = variance( 0.0 );
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// returns NaN
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v = variance( -1.5 );
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// returns NaN
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```
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</section>
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<!-- /.usage -->
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<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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</section>
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<!-- /.notes -->
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<!-- Package usage examples. -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var uniform = require( '@stdlib/random/array/uniform' );
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var variance = require( '@stdlib/stats/base/dists/bradford/variance' );
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var c = uniform( 10, 0.1, 10.0 );
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var v;
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var i;
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for ( i = 0; i < c.length; i++ ) {
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v = variance( c[ i ] );
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console.log( 'c: %d, Var(X;c): %d', c[ i ].toFixed( 4 ), v.toFixed( 4 ) );
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}
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```
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</section>
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<!-- /.examples -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[bradford-distribution]: https://en.wikipedia.org/wiki/Bradford%27s_law
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[variance]: https://en.wikipedia.org/wiki/Variance
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</section>
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<!-- /.links -->

Diff for: ‎lib/node_modules/@stdlib/stats/base/dists/bradford/variance/benchmark/benchmark.js

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2025 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var uniform = require( '@stdlib/random/array/uniform' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var pkg = require( './../package.json' ).name;
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var variance = require( './../lib' );
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// MAIN //
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bench( pkg, function benchmark( b ) {
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var c;
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var y;
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var i;
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c = uniform( 100, 0.1, 10.0 );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = variance( c[ i % c.length ] );
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if ( isnan( y ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( y ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});

Diff for: ‎lib/node_modules/@stdlib/stats/base/dists/bradford/variance/docs/img/equation_bradford_variance.svg

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

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{{alias}}( c )
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Returns the variance of a Bradford distribution with shape parameter `c`.
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If `c <= 0`, the function returns `NaN`.
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Parameters
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----------
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c: number
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Shape parameter.
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Returns
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-------
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out: number
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Variance.
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Examples
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--------
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> var v = {{alias}}( 0.1 )
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~0.083
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> v = {{alias}}( 0.5 )
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~0.083
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> v = {{alias}}( 10.0 )
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~0.076
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See Also
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--------
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Diff for: ‎lib/node_modules/@stdlib/stats/base/dists/bradford/variance/docs/types/index.d.ts

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/*
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* @license Apache-2.0
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*
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* Copyright (c) 2025 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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// TypeScript Version: 4.1
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/**
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* Returns the variance of a Bradford distribution.
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*
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* ## Notes
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*
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* - If `c <= 0`, the function returns `NaN`.
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*
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* @param c - shape parameter
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* @returns variance
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*
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* @example
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* var v = variance( 0.1 );
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* // returns ~0.083
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*
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* @example
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* var v = variance( 0.5 );
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* // returns ~0.083
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*
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* @example
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* var v = variance( 10.0 );
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* // returns ~0.076
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*
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* @example
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* var v = variance( 0.0 );
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* // returns NaN
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*
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* @example
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* var v = variance( -1.0 );
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* // returns NaN
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*
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* @example
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* var v = variance( NaN );
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* // returns NaN
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*/
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declare function variance( c: number ): number;
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// EXPORTS //
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export = variance;

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