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feat: add stats/base/dists/planck/cdf
PR-URL: #4130 Co-authored-by: Athan Reines <[email protected]> Reviewed-by: Athan Reines <[email protected]>
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‎lib/node_modules/@stdlib/stats/base/dists/planck/cdf/README.md

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<!--
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@license Apache-2.0
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Copyright (c) 2024 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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# Cumulative Distribution Function
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> Planck (discrete exponential) distribution [cumulative distribution function][cdf].
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<section class="intro">
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The [cumulative distribution function][cdf] for a Planck random variable is
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<!-- <equation class="equation" label="eq:planck_cdf" align="center" raw="F(x;\lambda) = 1 - e^{-\lambda \cdot (\lfloor x \rfloor + 1)}" alt="CDF for a Planck distribution."> -->
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```math
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F(x;\lambda) = 1 - e^{-\lambda (\lfloor x \rfloor + 1)}
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```
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<!-- </equation> -->
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where `λ` is the shape parameter and `x` denotes the count of events in a quantized system.
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var cdf = require( '@stdlib/stats/base/dists/planck/cdf' );
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```
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#### cdf( x, lambda )
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Evaluates the [cumulative distribution function][cdf] for a Planck (discrete exponential) distribution with shape parameter `lambda`.
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```javascript
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var y = cdf( 2.0, 0.5 );
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// returns ~0.7769
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y = cdf( 2.0, 1.5 );
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// returns ~0.9889
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```
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If provided `NaN` as any argument, the function returns `NaN`.
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```javascript
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var y = cdf( NaN, 0.5 );
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// returns NaN
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y = cdf( 0.0, NaN );
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// returns NaN
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```
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If provided a shape parameter `lambda` which is nonpositive, the function returns `NaN`.
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```javascript
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var y = cdf( 2.0, -1.0 );
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// returns NaN
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```
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#### cdf.factory( lambda )
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Returns a function for evaluating the [cumulative distribution function][cdf] of a Planck (discrete exponential) distribution with shape parameter `lambda`.
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```javascript
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var mycdf = cdf.factory( 1.5 );
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var y = mycdf( 3.0 );
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// returns ~0.9975
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y = mycdf( 1.0 );
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// returns ~0.9502
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```
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</section>
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<!-- /.usage -->
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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 discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
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var uniform = require( '@stdlib/random/array/uniform' );
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var cdf = require( '@stdlib/stats/base/dists/planck/cdf' );
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var x = discreteUniform( 10, 0, 5 );
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var lambda = uniform( 10, 0.1, 5.0 );
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var y;
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var i;
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for ( i = 0; i < lambda.length; i++ ) {
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y = cdf( x[ i ], lambda[ i ] );
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console.log( 'x: %d, λ: %d, F(x;λ): %d', x[ i ].toFixed( 4 ), lambda[ i ].toFixed( 4 ), y.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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[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/stats/base/dists/planck/cdf/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) 2024 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 discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
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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 cdf = require( './../lib' );
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// MAIN //
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bench( pkg, function benchmark( b ) {
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var lambda;
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var x;
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var y;
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var i;
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x = discreteUniform( 100, 0, 40 );
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lambda = 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 = cdf( x[ i % x.length ], lambda[ i % lambda.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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});
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bench( pkg+':factory', function benchmark( b ) {
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var mycdf;
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var x;
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var y;
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var i;
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x = discreteUniform( 100, 0, 40 );
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mycdf = cdf.factory( 0.3 );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = mycdf( x[ i % x.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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});

‎lib/node_modules/@stdlib/stats/base/dists/planck/cdf/docs/repl.txt

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{{alias}}( x, λ )
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Evaluates the cumulative distribution function (CDF) for a Planck
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distribution with shape parameter `λ` at a value `x`.
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If provided `NaN` as any argument, the function returns `NaN`.
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If `λ <= 0`, the function returns `NaN`.
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Parameters
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----------
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x: number
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Input value.
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λ: 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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Evaluated CDF.
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Examples
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--------
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> var y = {{alias}}( 2.0, 0.5 )
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~0.7769
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> y = {{alias}}( 2.0, 1.5 )
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~0.9889
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> y = {{alias}}( -1.0, 4.0 )
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0.0
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> y = {{alias}}( NaN, 0.5 )
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NaN
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> y = {{alias}}( 0.0, NaN )
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NaN
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// Invalid shape parameter
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> y = {{alias}}( 2.0, -1.4 )
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NaN
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{{alias}}.factory( λ )
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Returns a function for evaluating the cumulative distribution function (CDF)
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of a Planck distribution with shape parameter `λ`.
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Parameters
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----------
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λ: number
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Shape parameter.
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Returns
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-------
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cdf: Function
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Cumulative distribution function (CDF).
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Examples
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--------
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> var mycdf = {{alias}}.factory( 1.5 );
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> var y = mycdf( 3.0 )
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~0.9975
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> y = mycdf( 1.0 )
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~0.9502
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See Also
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--------
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‎lib/node_modules/@stdlib/stats/base/dists/planck/cdf/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) 2024 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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* Evaluates the cumulative distribution function (CDF) for a Planck distribution.
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*
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* @param x - input value
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* @returns evaluated CDF
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*/
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type Unary = ( x: number ) => number;
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/**
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* Interface for the cumulative distribution function (CDF) of a Planck distribution.
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*/
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interface CDF {
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/**
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* Evaluates the cumulative distribution function (CDF) for a Planck distribution with shape parameter `lambda` at a value `x`.
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*
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* ## Notes
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*
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* - If `lambda <= 0`, the function returns `NaN`.
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*
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* @param x - input value
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* @param lambda - shape parameter
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* @returns evaluated CDF
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*
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* @example
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* var y = cdf( 2.0, 0.5 );
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* // returns ~0.7769
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*
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* @example
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* var y = cdf( 2.0, 1.5 );
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* // returns ~0.9889
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*
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* @example
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* var y = cdf( -1.0, 0.5 );
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* // returns 0.0
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*
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* @example
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* var y = cdf( NaN, 0.5 );
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* // returns NaN
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*
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* @example
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* var y = cdf( 0.0, NaN );
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* // returns NaN
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*
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* @example
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* // Invalid probability
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* var y = cdf( 2.0, 1.4 );
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* // returns NaN
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*/
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( x: number, lambda: number ): number;
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/**
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* Returns a function for evaluating the cumulative distribution function (CDF) for a Planck distribution with shape parameter `lambda`.
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*
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* @param lambda - shape parameter
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* @returns CDF
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*
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* @example
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* var mycdf = cdf.factory( 1.5 );
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* var y = mycdf( 3.0 );
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* // returns ~0.9975
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*
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* y = mycdf( 1.0 );
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* // returns ~0.9502
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*/
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factory( lambda: number ): Unary;
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}
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/**
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* Planck distribution cumulative distribution function (CDF).
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*
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* @param x - input value
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* @param lambda - shape parameter
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* @returns evaluated CDF
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*
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* @example
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* var y = cdf( 2.0, 0.5 );
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* // returns ~0.7769
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*
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* y = cdf( 2.0, 1.5 );
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* // returns ~0.9889
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*
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* var mycdf = cdf.factory( 1.5 );
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* y = mycdf( 3.0 );
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* // returns ~0.9975
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*
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* y = mycdf( 1.0 );
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* // returns ~0.9502
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*/
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declare var cdf: CDF;
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// EXPORTS //
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export = cdf;

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