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feat: add stats/base/dists/planck/mgf
PR-URL: #4478 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/mgf/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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# Moment-Generating Function
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> Planck (discrete exponential) distribution moment-generating function (MGF).
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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 [moment-generating function][mgf] for a Planck random variable is
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<!-- <equation class="equation" label="eq:planck_mgf_function" align="center" raw="M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = \frac{1 - e^{-\lambda}}{1 - e^{t - \lambda}}" alt="Moment-generating function (MGF) for the Planck distribution."> -->
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```math
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M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = \frac{1 - e^{-\lambda}}{1 - e^{t - \lambda}}
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```
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<!-- </equation> -->
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where `λ` 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 mgf = require( '@stdlib/stats/base/dists/planck/mgf' );
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```
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#### mgf( t, lambda )
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Evaluates the moment-generating function ([MGF][mgf]) of a Planck (discrete exponential) distribution with shape parameter `lambda`.
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```javascript
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var y = mgf( 0.2, 0.5 );
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// returns ~1.5181
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y = mgf( 0.4, 1.5 );
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// returns ~1.1645
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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 = mgf( NaN, 0.0 );
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// returns NaN
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y = mgf( 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 = mgf( 2.0, -1.0 );
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// returns NaN
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```
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#### mgf.factory( lambda )
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Returns a function for evaluating the [moment-generating function][mgf] of a Planck (discrete exponential) distribution with shape parameter `lambda`.
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```javascript
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var mymgf = mgf.factory( 0.8 );
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var y = mymgf( -0.2 );
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// returns ~0.8711
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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 mgf = require( '@stdlib/stats/base/dists/planck/mgf' );
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var lambda = uniform( 10, 0.1, 5.0 );
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var t = uniform( 10, 0.0, 10.0 );
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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 = mgf( t[ i ], lambda[ i ] );
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console.log( 't: %d, λ: %d, M_X(t;λ): %d', t[ 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 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. -->
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<section class="references">
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</section>
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<!-- /.references -->
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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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[mgf]: https://en.wikipedia.org/wiki/Moment-generating_function
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/stats/base/dists/planck/mgf/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 mgf = 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 t;
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var y;
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var i;
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lambda = uniform( 100, 0.1, 10.0 );
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t = uniform( 100, 0.0, 10.0 );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = mgf( t[ i % t.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 mymgf;
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var t;
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var y;
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var i;
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t = uniform( 100, 0.0, 10.0 );
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mymgf = mgf.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 = mymgf( t[ i % t.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/mgf/docs/repl.txt

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{{alias}}( t, λ )
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Evaluates the moment-generating function (MGF) for a Planck distribution
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with shape parameter `λ` at a value `t`.
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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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t: 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 MGF.
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Examples
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--------
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> var y = {{alias}}( 0.2, 0.5 )
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~1.5181
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> y = {{alias}}( 0.4, 1.5 )
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~1.1645
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> y = {{alias}}( NaN, 0.0 )
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NaN
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> y = {{alias}}( 0.0, NaN )
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NaN
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> y = {{alias}}( 2.0, -1.0 )
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NaN
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{{alias}}.factory( λ )
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Returns a function for evaluating the moment-generating function (MGF) of a
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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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mgf: Function
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Moment-generating function (MGF).
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Examples
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--------
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> var mymgf = {{alias}}.factory( 0.8 );
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> var y = mymgf( -0.2 )
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~0.8711
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See Also
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--------
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