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

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lib/node_modules/@stdlib/stats/base/dists/planck/variance/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2024 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.
+
+-->
+
+# Variance
+
+> Planck 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 Planck random variable is
+
+<!-- <equation class="equation" label="eq:planck_variance" align="center" raw="\operatorname{Var}\left( X \right) = \frac{e^{-\lambda}}{\left( 1 - e^{-\lambda} \right)^{2}}" alt="Variance for a Planck distribution."> -->
+
+```math
+\mathop{\mathrm{Var}}\left( X \right) = \frac{e^{-\lambda}}{\left( 1 - e^{-\lambda} \right)^{2}}
+```
+
+<!-- </equation> -->
+
+where `lambda` is the shape parameter.
+
+</section>
+
+<!-- /.intro -->
+
+<!-- Package usage documentation. -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var variance = require( '@stdlib/stats/base/dists/planck/variance' );
+```
+
+#### variance( lambda )
+
+Returns the [variance][variance] of a Planck distribution with shape parameter `lambda`.
+
+```javascript
+var v = variance( 0.1 );
+// returns ~99.9167
+
+v = variance( 1.5 );
+// returns ~0.3697
+```
+
+If provided a success probability `lambda` which is negative, the function returns `NaN`.
+
+```javascript
+var v = variance( NaN );
+// returns NaN
+
+v = variance( -1.0 );
+// 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/planck/variance' );
+
+var lambda;
+var v;
+var i;
+
+lambda = uniform( 10, 0.0, 10.0 );
+
+for ( i = 0; i < 10; i++ ) {
+    v = variance( lambda[ i ] );
+    console.log( 'lambda: %d, Var(X;lambda): %d', lambda[ i ].toFixed( 4 ), v.toFixed( 4 ) );
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="references">
+
+</section>
+
+<!-- /.references -->
+
+<!-- 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">
+
+[variance]: https://en.wikipedia.org/wiki/Variance
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/stats/base/dists/planck/variance/benchmark/benchmark.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 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 lambda;
+	var y;
+	var i;
+
+	lambda = uniform( 100, 0.0, 10.0 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = variance( lambda[ i % lambda.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/planck/variance/docs/repl.txt

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+
+{{alias}}( lambda )
+    Returns the variance of a Planck distribution with shape parameter
+    `lambda`.
+
+    If `lambda < 0`, the function returns `NaN`.
+
+    Parameters
+    ----------
+    lambda: number
+        Shape parameter.
+
+    Returns
+    -------
+    out: number
+        Variance.
+
+    Examples
+    --------
+    > var v = {{alias}}( 0.1 )
+    ~99.9167
+    > v = {{alias}}( 1.5 )
+    ~0.3697
+
+    See Also
+    --------
+

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

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+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2024 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 Planck distribution.
+*
+* ## Notes
+*
+* -   If `lambda < 0`, the function returns `NaN`.
+*
+* @param lambda - shape parameter
+* @returns variance
+*
+* @example
+* var v = variance( 0.1 );
+* // returns ~99.9167
+*
+* @example
+* var v = variance( 1.5 );
+* // returns ~0.3697
+*
+* @example
+* var v = variance( -1.0 );
+* // returns NaN
+*
+* @example
+* var v = variance( NaN );
+* // returns NaN
+*/
+declare function variance( lambda: number ): number;
+
+
+// EXPORTS //
+
+export = variance;

lib/node_modules/@stdlib/stats/base/dists/planck/variance/docs/types/test.ts

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+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2024 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.
+*/
+
+import variance = require( './index' );
+
+
+// TESTS //
+
+// The function returns a number...
+{
+	variance( 0.3 ); // $ExpectType number
+}
+
+// The compiler throws an error if the function is provided a value other than a number...
+{
+	variance( true ); // $ExpectError
+	variance( false ); // $ExpectError
+	variance( null ); // $ExpectError
+	variance( undefined ); // $ExpectError
+	variance( '5' ); // $ExpectError
+	variance( [] ); // $ExpectError
+	variance( {} ); // $ExpectError
+	variance( ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided insufficient arguments...
+{
+	variance(); // $ExpectError
+}

lib/node_modules/@stdlib/stats/base/dists/planck/variance/examples/index.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 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';
+
+var uniform = require( '@stdlib/random/array/uniform' );
+var variance = require( './../lib' );
+
+var lambda;
+var v;
+var i;
+
+lambda = uniform( 10, 0.0, 10.0 );
+
+for ( i = 0; i < 10; i++ ) {
+	v = variance( lambda[ i ] );
+	console.log( 'lambda: %d, Var(X;lambda): %d', lambda[ i ].toFixed( 4 ), v.toFixed( 4 ) );
+}

lib/node_modules/@stdlib/stats/base/dists/planck/variance/lib/index.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 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';
+
+/**
+* Planck distribution variance.
+*
+* @module @stdlib/stats/base/dists/planck/variance
+*
+* @example
+* var variance = require( '@stdlib/stats/base/dists/planck/variance' );
+*
+* var v = variance( 0.1 );
+* // returns ~99.9167
+*
+* v = variance( 1.5 );
+* // returns ~0.3697
+*/
+
+// MODULES //
+
+var main = require( './main.js' );
+
+
+// EXPORTS //
+
+module.exports = main;