feat: added stats/base/dists/boltzmann/pmf

lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/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.
+
+-->
+
+# Probability Mass Function
+
+> [Boltzmann][boltzmann-distribution] distribution probability mass function (PMF).
+
+<section class="intro">
+
+The [probability mass function][pmf] (PMF) for a [boltzmann][boltzmann-distribution] random variable is
+
+```math
+f(x; \lambda, N) = P(X=x; \lambda, N) = \begin{cases}
+\frac{{(\exp(-\lambda k))}{(1-\exp(-\lambda))}}{{(1-\exp(-\lambda N))}} & \text{for } k = 0, 1, 2, \ldots, N \\0 & \text{otherwise}
+\end{cases}
+```
+
+where `λ` is the inverse temperature parameter (equal to `1/KbT`) and `N` is the total number of energy states in the system.
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var pmf = require( '@stdlib/stats/base/dists/boltzmann/pmf' );
+```
+
+#### pmf( x, λ, N )
+
+Evaluates the [probability mass function][pmf] (PMF) for a [boltzmann][boltzmann-distribution] distribution with total number of energy states `N` and inverse temperature parameter `λ`.
+
+```javascript
+var y = pmf( 1, 0.8, 4 );
+// returns ~0.258
+
+y = pmf( 2, 0.8, 4 );
+// returns ~0.116
+
+y = pmf( 0, 0.8, 4 );
+// returns ~0.574
+```
+
+If provided `NaN` as any argument, the function returns `NaN`.
+
+```javascript
+var y = pmf( NaN, 1.5, 5 );
+// returns NaN
+
+y = pmf( 2, NaN, 5 );
+// returns NaN
+
+y = pmf( 2, 1.5, NaN );
+// returns NaN
+```
+
+If provided total number if energy states `N` is not a nonnegative integer, the function returns `NaN`.
+
+```javascript
+var y = pmf( 2, 1.5, 4.5 );
+// returns NaN
+
+y = pmf( 2, 2.0, -5 );
+// returns NaN
+```
+
+If provided inverse temperature parameter `λ` is not a positive number, the function returns `NaN`.
+
+```javascript
+var y = pmf( 8, -2.5, 15 );
+// returns NaN
+```
+
+#### pmf.factory( λ, N )
+
+Returns a function for evaluating the [probability mass function][pmf] (PMF) of a [boltzmann][boltzmann-distribution] distribution with total number of energy states `N` and inverse Temperature `λ`.
+
+```javascript
+var mypmf = pmf.factory( 1.4, 8 );
+
+var y = mypmf( 3 );
+// returns ~0.011
+
+y = mypmf( 1 );
+// returns ~0.186
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var randu = require( '@stdlib/random/base/randu' );
+var round = require( '@stdlib/math/base/special/round' );
+var pmf = require( '@stdlib/stats/base/dists/boltzmann/pmf' );
+
+var N;
+var lambda;
+var x;
+var y;
+var i;
+
+for ( i = 0; i < 10; i++ ) {
+    N = round( randu() * 20 );
+    x = round( randu() * N );
+    lambda = randu();
+    y = pmf( x, lambda, N );
+    console.log( 'x: %d, λ: %d, N: %d, P(X = x;λ,N): %d', x, lambda.toFixed( 4 ), N, y.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">
+
+[boltzmann-distribution]: https://en.wikipedia.org/wiki/Boltzmann_distribution
+[pmf]: https://en.wikipedia.org/wiki/Probability_mass_function
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/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 round = require( '@stdlib/math/base/special/round' );
+var randu = require( '@stdlib/random/base/randu' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pkg = require( './../package.json' ).name;
+var pmf = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var lambda;
+	var N;
+	var x;
+	var y;
+	var i;
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		lambda = randu();
+		N = round( randu()*20 );
+		x = round( randu()*N );
+		y = pmf( x, lambda, N );
+		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();
+});
+
+bench( pkg+':factory', function benchmark( b ) {
+	var lambda;
+	var mypmf;
+	var N;
+	var x;
+	var i;
+	var y;
+
+	lambda = randu();
+	N = round( randu()*20 );
+	mypmf = pmf.factory( lambda, N );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		x = round( randu()*N );
+		y = mypmf( x );
+		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/boltzmann/pmf/docs/repl.txt

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+
+{{alias}}( x, λ, N )
+    Evaluates the probability mass function (PMF) for a boltzmann
+    distribution with total number of energy states `N` and inverse 
+    temperature analysis `λ` at a value `x`.
+
+    If provided `NaN` as any argument, the function returns `NaN`.
+
+    If provided total number of energy states `N`, inverse temperature 
+    parameter `λ` or draws `n` which is not a nonnegative integer,
+    the function returns `NaN`.
+
+    Parameters
+    ----------
+    x: integer
+        Input value.
+
+    λ: number
+        Inverse temperature parameter.
+
+    N: integer
+        Total number of energy states.
+
+    Returns
+    -------
+    out: number
+        Evaluated PMF.
+
+    Examples
+    --------
+    > var y = {{alias}}( 1, 0.8, 4 )
+    ~0.258
+    > y = {{alias}}( 2, 0.8, 4 )
+    ~0.116
+    > y = {{alias}}( 0, 0.8, 4 )
+    ~0.574
+
+    > y = {{alias}}( NaN, 1.5, 5 )
+    NaN
+    > y = {{alias}}( 2, NaN, 5 )
+    NaN
+    > y = {{alias}}( 2, 1.5, NaN )
+    NaN
+
+    > y = {{alias}}( 2, 1.5, 4.5 )
+    NaN
+    > y = {{alias}}( 2, 1.5, -2 )
+    NaN
+    > y = {{alias}}( 2, -1.5, 5 )
+    NaN
+
+
+{{alias}}.factory( λ, N )
+    Returns a function for evaluating the probability mass function (PMF) of a
+    boltzmann distribution with total number of energy states `N`, and 
+    inverse temperature parameter `λ`.
+
+    Parameters
+    ----------
+    λ: number
+        Inverse temperature parameter.
+
+    N: integer
+        Total number of energy states.
+
+    Returns
+    -------
+    pmf: Function
+        Probability mass function (PMF).
+
+    Examples
+    --------
+    > var myPMF = {{alias}}.factory( 1.4, 8 );
+    > var y = myPMF( 3 )
+    ~0.011
+    > y = myPMF( 1.0 )
+    ~0.186
+
+    See Also
+    --------