diff --git a/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/README.md b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/README.md
new file mode 100644
index 00000000000..0e591399aeb
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/README.md
@@ -0,0 +1,159 @@
+
+
+# Probability Mass Function
+
+> [Boltzmann][boltzmann-distribution] distribution probability mass function (PMF).
+
+
+
+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.
+
+
+
+
+
+
+
+## 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
+```
+
+
+
+
+
+
+
+## Examples
+
+
+
+```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 ) );
+}
+```
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+[boltzmann-distribution]: https://en.wikipedia.org/wiki/Boltzmann_distribution
+[pmf]: https://en.wikipedia.org/wiki/Probability_mass_function
+
+
+
+
diff --git a/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/benchmark/benchmark.js b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/benchmark/benchmark.js
new file mode 100644
index 00000000000..cdf9407c03e
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/benchmark/benchmark.js
@@ -0,0 +1,84 @@
+/**
+* @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();
+});
diff --git a/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/docs/repl.txt b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/docs/repl.txt
new file mode 100644
index 00000000000..85c99eafad9
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/docs/repl.txt
@@ -0,0 +1,80 @@
+
+{{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
+ --------
diff --git a/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/docs/types/index.d.ts b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/docs/types/index.d.ts
new file mode 100644
index 00000000000..93d0a5d8869
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/docs/types/index.d.ts
@@ -0,0 +1,130 @@
+/*
+* @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
+
+/**
+* Evaluates the probability mass function (PMF) for a boltzmann distribution.
+*
+* @param x - input value
+* @returns evaluated PMF
+*/
+type Unary = ( x: number ) => number;
+
+/**
+* Interface for the probability mass function (PMF) of a boltzmann distribution.
+*/
+interface PMF {
+ /**
+ * Evaluates the probability mass function (PMF) for a boltzmann distribution with total number of energy states `N`, and inverse temperature parameter `λ`.
+ *
+ * ## Notes
+ *
+ * - If provided a total number of energy states `N` and inverse temperature parameter `λ` which is not a nonnegative integer, the function returns `NaN`.
+ *
+ * @param x - input value
+ * @param N - total number of energy states
+ * @param lambda - inverse temperature parameter
+ * @returns evaluated PMF
+ *
+ * @example
+ * var y = pmf( 1, 8, 4 );
+ * // returns ~0.257
+ *
+ * @example
+ * var y = pmf( 2, 8, 4 );
+ * // returns ~0.115
+ *
+ * @example
+ * var y = pmf( 0, 8, 4 );
+ * // returns ~0.574
+ *
+ * @example
+ * var y = pmf( 5, 8, 4 );
+ * // returns 0.0
+ *
+ * @example
+ * var y = pmf( NaN, 1.5, 5 );
+ * // returns NaN
+ *
+ * @example
+ * var y = pmf( 2, NaN, 5 );
+ * // returns NaN
+ *
+ * @example
+ * var y = pmf( 2, 1.5, NaN );
+ * // returns NaN
+ *
+ * @example
+ * var y = pmf( 2, 1.5, 4.5 );
+ * // returns NaN
+ *
+ * @example
+ * var y = pmf( 2, 1.5, -5 );
+ * // returns NaN
+ *
+ * @example
+ * var y = pmf( 2, -1.5, 5 );
+ * // returns NaN
+ *
+ * @example
+ * var y = pmf( 5.2, 10, 5 );
+ * // returns NaN
+ */
+ ( x: number, lambda: number, N: number ): number;
+
+ /**
+ * Returns a function for evaluating the probability mass function (PMF) for a boltzmann distribution with total number of energy states `N`, and inverse temperature parameter `λ`.
+ *
+ * @param N - total number of energy states
+ * @param lambda - inverse temperature parameter
+ * @returns PMF
+ *
+ * @example
+ * var mypmf = pmf.factory( 1.4, 8 );
+ * var y = mypmf( 3 );
+ * // returns ~0.011
+ *
+ * y = mypmf( 1 );
+ * // returns ~0.185
+ */
+ factory( N: number, lambda: number ): Unary;
+}
+
+/**
+* Boltzmann distribution probability mass function (PMF).
+*
+* @param x - input value
+* @param N - total states of energy
+* @param lambda - inverse temperature parameter
+* @returns evaluated PMF
+*
+* @example
+* var mypmf = pmf.factory( 1.2, 10 );
+* y = mypmf( 4 );
+* // returns ~0.0.57
+*
+* y = mypmf( 1 );
+* // returns ~0.2104
+*/
+declare var pmf: PMF;
+
+
+// EXPORTS //
+
+export = pmf;
diff --git a/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/docs/types/test.ts b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/docs/types/test.ts
new file mode 100644
index 00000000000..ae2881fb3f9
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/docs/types/test.ts
@@ -0,0 +1,119 @@
+/*
+* @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 pmf = require( './index' );
+
+
+// TESTS //
+
+// The function returns a number...
+{
+ pmf( 2, 10, 4 ); // $ExpectType number
+ pmf( 1, 10, 8 ); // $ExpectType number
+}
+
+// The compiler throws an error if the function is provided values other than four numbers...
+{
+ pmf( true, 10, 6 ); // $ExpectError
+ pmf( false, 10, 4 ); // $ExpectError
+ pmf( '5', 10, 2 ); // $ExpectError
+ pmf( [], 10, 2 ); // $ExpectError
+ pmf( {}, 10, 4 ); // $ExpectError
+ pmf( ( x: number ): number => x, 2, 4 ); // $ExpectError
+
+ pmf( 9, true, 12 ); // $ExpectError
+ pmf( 9, false, 12 ); // $ExpectError
+ pmf( 5, '5', 10 ); // $ExpectError
+ pmf( 8, [], 16 ); // $ExpectError
+ pmf( 9, {}, 18 ); // $ExpectError
+ pmf( 8, ( x: number ): number => x, 16 ); // $ExpectError
+
+ pmf( 9, 5, true ); // $ExpectError
+ pmf( 9, 5, false ); // $ExpectError
+ pmf( 5, 2, '5' ); // $ExpectError
+ pmf( 8, 4, [] ); // $ExpectError
+ pmf( 9, 4, {} ); // $ExpectError
+ pmf( 8, 5, ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided an unsupported number of arguments...
+{
+ pmf(); // $ExpectError
+ pmf( 2 ); // $ExpectError
+ pmf( 2, 10 ); // $ExpectError
+ pmf( 2, 10, 4, 1, 5 ); // $ExpectError
+}
+
+// Attached to main export is a `factory` method which returns a function...
+{
+ pmf.factory( 13, 5 ); // $ExpectType Unary
+}
+
+// The `factory` method returns a function which returns a number...
+{
+ const fcn = pmf.factory( 13, 5 );
+ fcn( 2 ); // $ExpectType number
+}
+
+// The compiler throws an error if the function returned by the `factory` method is provided invalid arguments...
+{
+ const fcn = pmf.factory( 13, 5 );
+ fcn( true ); // $ExpectError
+ fcn( false ); // $ExpectError
+ fcn( '5' ); // $ExpectError
+ fcn( [] ); // $ExpectError
+ fcn( {} ); // $ExpectError
+ fcn( ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the function returned by the `factory` method is provided an unsupported number of arguments...
+{
+ const fcn = pmf.factory( 13, 5 );
+ fcn(); // $ExpectError
+ fcn( 2, 0 ); // $ExpectError
+ fcn( 2, 0, 1 ); // $ExpectError
+}
+
+// The compiler throws an error if the `factory` method is provided values other than three numbers..
+{
+ pmf.factory( true, 3 ); // $ExpectError
+ pmf.factory( false, 3 ); // $ExpectError
+ pmf.factory( '5', 1 ); // $ExpectError
+ pmf.factory( [], 1 ); // $ExpectError
+ pmf.factory( {}, 2 ); // $ExpectError
+ pmf.factory( ( x: number ): number => x, 2 ); // $ExpectError
+
+ pmf.factory( 9, true ); // $ExpectError
+ pmf.factory( 9, false ); // $ExpectError
+ pmf.factory( 5, '5' ); // $ExpectError
+ pmf.factory( 8, [] ); // $ExpectError
+ pmf.factory( 9, {} ); // $ExpectError
+ pmf.factory( 8, ( x: number ): number => x ); // $ExpectError
+
+ pmf.factory( [], true ); // $ExpectError
+ pmf.factory( {}, false ); // $ExpectError
+ pmf.factory( false, '5' ); // $ExpectError
+ pmf.factory( {}, [] ); // $ExpectError
+ pmf.factory( '5', ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the `factory` method is provided an unsupported number of arguments...
+{
+ pmf.factory( 10 ); // $ExpectError
+ pmf.factory( 10, 4, 3, 7 ); // $ExpectError
+}
diff --git a/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/example/index.js b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/example/index.js
new file mode 100644
index 00000000000..abf6198e399
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/example/index.js
@@ -0,0 +1,37 @@
+/**
+* @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 randu = require( '@stdlib/random/base/randu' );
+var round = require( '@stdlib/math/base/special/round' );
+var pmf = require( './../lib' );
+
+var i;
+var N;
+var lambda;
+var x;
+var y;
+
+for ( i = 0; i < 10; i++ ) {
+ lambda = randu();
+ N = round( randu() * 20.0 );
+ x = round( randu() * N );
+ 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 ) );
+}
diff --git a/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/lib/factory.js b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/lib/factory.js
new file mode 100644
index 00000000000..fa89efe4afc
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/lib/factory.js
@@ -0,0 +1,89 @@
+/**
+* @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 isNonNegativeInteger = require( '@stdlib/math/base/assert/is-nonnegative-integer' );
+var isNonNegativeFinite = require( '@stdlib/math/base/assert/is-nonnegative-finite' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var constantFunction = require( '@stdlib/utils/constant-function' );
+var exp = require( '@stdlib/math/base/special/exp' );
+var PINF = require( '@stdlib/constants/float64/pinf' );
+
+
+// MAIN //
+
+/**
+* Returns a function for evaluating the probability mass function (PMF) for a Boltzmann distribution with total number of energy states `N`, and the inverse temperature `lambda`.
+*
+* @param {PositiveNumber} lambda - Inverse Temperature
+* @param {NonNegativeInteger} N - Total Number of energy states
+* @returns {Function} PMF
+*
+* @example
+* var mypmf = factory( 1.2, 10 );
+* var y = mypmf( 4 );
+* // returns ~0.0058
+*
+* y = mypmf( 1 );
+* // returns ~0.2105
+*/
+function factory( lambda, N ) {
+ if (
+ isnan( N ) ||
+ isnan( lambda ) ||
+ !isNonNegativeInteger( N ) ||
+ !isNonNegativeFinite( lambda ) ||
+ N === PINF ||
+ lambda === PINF
+ ) {
+ return constantFunction( NaN );
+ }
+
+ return pmf;
+
+ /**
+ * Evaluates the probability mass function (PMF) for a Boltzmann distribution.
+ *
+ * @private
+ * @param {number} x - input value
+ * @returns {Probability} evaluated PMF
+ */
+ function pmf( x ) {
+ var fact;
+
+ if ( isnan( x ) ) {
+ return NaN;
+ }
+ if (
+ isNonNegativeInteger( x ) &&
+ x < N
+ ) {
+ fact = ( 1 - exp( -lambda ) ) / ( 1 - exp( -lambda * N ) );
+ return fact * exp( -lambda * x );
+ }
+ return 0.0;
+ }
+}
+
+
+// EXPORTS //
+
+module.exports = factory;
diff --git a/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/lib/index.js b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/lib/index.js
new file mode 100644
index 00000000000..49d75e3b72e
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/lib/index.js
@@ -0,0 +1,60 @@
+/**
+* @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';
+
+/**
+* Boltzmann distribution probability mass function (PMF).
+*
+* @module @stdlib/stats/base/dists/boltzmann/pmf
+*
+* @example
+* var pmf = require( '@stdlib/stats/base/dists/boltzmann/pmf' );
+*
+* var y = pmf( 1, 0.8, 4 );
+* // returns ~0.257
+*
+* y = pmf( 2, 0.8, 4 );
+* // returns ~0.115
+*
+* y = pmf( 0, 0.8, 4 );
+* // returns ~0.574
+*
+* var mypmf = pmf.factory( 1.5, 5 );
+* y = mypmf( 4.0 );
+* // returns ~0.0019
+*
+* y = mypmf( 1.0 );
+* // returns ~0.173
+*/
+
+// MODULES //
+
+var setReadOnly = require( '@stdlib/utils/define-nonenumerable-read-only-property' );
+var main = require( './main.js' );
+var factory = require( './factory.js' );
+
+
+// MAIN //
+
+setReadOnly( main, 'factory', factory );
+
+
+// EXPORTS //
+
+module.exports = main;
diff --git a/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/lib/main.js b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/lib/main.js
new file mode 100644
index 00000000000..4d9c5dd3a55
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/lib/main.js
@@ -0,0 +1,105 @@
+/**
+* @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 isNonNegativeInteger = require( '@stdlib/math/base/assert/is-nonnegative-integer' );
+var isNonNegativeFinite = require( '@stdlib/math/base/assert/is-nonnegative-finite' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var exp = require( '@stdlib/math/base/special/exp' );
+var PINF = require( '@stdlib/constants/float64/pinf' );
+
+
+// MAIN //
+
+/**
+* Returns a function for evaluating the probability mass function (PMF) for a Boltzmann distribution with total number of energy states `N`, and the inverse temperature `lambda`.
+*
+* @param {NonNegativeInteger} x - Input value of energy
+* @param {PositiveNumber} lambda - Inverse Temperature
+* @param {NonNegativeInteger} N - Total Number of energy states
+* @returns {Function} PMF
+*
+* @example
+* var y = pmf( 1, 0.8, 4 );
+* // returns ~0.258
+*
+* @example
+* y = pmf( 2, 0.8, 4 );
+* // returns ~0.116
+*
+* @example
+* y = pmf( 0, 0.8, 4 );
+* // returns ~0.574
+*
+* @example
+* var y = pmf( NaN, 0.5, 5 );
+* // returns NaN
+*
+* @example
+* var y = pmf( 2, NaN, 5 );
+* // returns NaN
+*
+* @example
+* var y = pmf( 2, 0.8, NaN );
+* // returns NaN
+*
+* @example
+* var y = pmf( 2.0, -10.5, 5 );
+* // returns NaN
+*
+* @example
+* var y = pmf( 2.0, 5, 1.5 );
+* // returns NaN
+*
+* @example
+* var y = pmf( 6.0, 0.8, 5 )
+* // return 0.0
+*
+*/
+function pmf( x, lambda, N ) {
+ var fact;
+
+ if (
+ isnan( x ) ||
+ isnan( N ) ||
+ isnan( lambda ) ||
+ !isNonNegativeInteger( N ) ||
+ !isNonNegativeInteger( x ) ||
+ !isNonNegativeFinite( lambda ) ||
+ N === PINF ||
+ lambda === PINF
+ ) {
+ return NaN;
+ }
+ if (
+ isNonNegativeInteger( x ) &&
+ x < N
+ ) {
+ fact = ( 1 - exp( -lambda ) ) / ( 1 - exp( -lambda * N ) );
+ return fact * exp( -lambda * x );
+ }
+ return 0.0;
+}
+
+
+// EXPORTS //
+
+module.exports = pmf;
diff --git a/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/package.json b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/package.json
new file mode 100644
index 00000000000..be27a77e12b
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/package.json
@@ -0,0 +1,64 @@
+{
+ "name": "@stdlib/stats/base/dists/boltzmann/pmf",
+ "version": "0.0.0",
+ "description": "Boltzmann distribution probability mass function (PMF).",
+ "license": "Apache-2.0",
+ "author": {
+ "name": "The Stdlib Authors",
+ "url": "https://github.com/stdlib-js/stdlib/graphs/contributors"
+ },
+ "contributors": [
+ {
+ "name": "The Stdlib Authors",
+ "url": "https://github.com/stdlib-js/stdlib/graphs/contributors"
+ }
+ ],
+ "main": "./lib",
+ "directories": {
+ "benchmark": "./benchmark",
+ "doc": "./docs",
+ "example": "./examples",
+ "lib": "./lib",
+ "test": "./test"
+ },
+ "types": "./docs/types",
+ "scripts": {},
+ "homepage": "https://github.com/stdlib-js/stdlib",
+ "repository": {
+ "type": "git",
+ "url": "git://github.com/stdlib-js/stdlib.git"
+ },
+ "bugs": {
+ "url": "https://github.com/stdlib-js/stdlib/issues"
+ },
+ "dependencies": {},
+ "devDependencies": {},
+ "engines": {
+ "node": ">=0.10.0",
+ "npm": ">2.7.0"
+ },
+ "os": [
+ "aix",
+ "darwin",
+ "freebsd",
+ "linux",
+ "macos",
+ "openbsd",
+ "sunos",
+ "win32",
+ "windows"
+ ],
+ "keywords": [
+ "stdlib",
+ "stdmath",
+ "statistics",
+ "stats",
+ "distribution",
+ "dist",
+ "probability",
+ "pmf",
+ "hypergeometric",
+ "univariate",
+ "discrete"
+ ]
+ }
\ No newline at end of file
diff --git a/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/test/fixtures/julia/REQUIRE b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/test/fixtures/julia/REQUIRE
new file mode 100644
index 00000000000..b95eaf528e9
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/test/fixtures/julia/REQUIRE
@@ -0,0 +1,3 @@
+Distributions 0.23.8
+julia 1.5
+JSON 0.21
\ No newline at end of file
diff --git a/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/test/fixtures/julia/data.json b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/test/fixtures/julia/data.json
new file mode 100644
index 00000000000..4bedce412a1
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/test/fixtures/julia/data.json
@@ -0,0 +1,210 @@
+{
+ "expected": [
+ 1.6894024658203856e-08,
+ 0.0017111735253480995,
+ 4.335124169281193e-06,
+ 1.4137977957263547e-08,
+ 9.297737679321286e-07,
+ 1.4340917335819795e-08,
+ 1.195748460493818e-10,
+ 6.561413624202478e-14,
+ 2.516786068799857e-06,
+ 2.799398817837934e-11,
+ 1.0572291019068076e-05,
+ 3.77023451376494e-09,
+ 0.222036849409128,
+ 0.19743936971721374,
+ 7.567022726893674e-12,
+ 4.068498556625846e-08,
+ 1.388323939572844e-12,
+ 1.8104201808034692e-07,
+ 8.762739789129443e-14,
+ 0.1295631741766526,
+ 0.0006401229790481351,
+ 9.708689970886001e-08,
+ 4.7832281543773015e-05,
+ 0.00012297924148380054,
+ 3.6658796729520696e-06,
+ 1.0811991791156922e-09,
+ 6.034361062893161e-08,
+ 0.0053704747063018695,
+ 0.0032582790209853283,
+ 4.573380515881846e-11,
+ 0.13093186067155696,
+ 0.09844632997256281,
+ 9.556070157676168e-10,
+ 3.547489846106477e-11,
+ 2.599529476727121e-05,
+ 0.006153547432807735,
+ 1.8230372131433778e-06,
+ 0.23523369402522293,
+ 8.785402815409199e-10,
+ 2.7886419606076006e-09,
+ 1.2258706960139622e-08,
+ 8.394338901630111e-10,
+ 8.423218070966707e-13,
+ 8.609172869784758e-06,
+ 8.58541500699885e-08,
+ 0.23487252294206842,
+ 1.4931141842151473e-11,
+ 3.004761984595269e-06,
+ 0.0302949574244473,
+ 2.986606901465607e-13
+ ],
+ "lambda": [
+ 1.6065861904183274,
+ 3.1636935985364647,
+ 1.338283136043986,
+ 3.003922854186611,
+ 2.297058002327272,
+ 1.3666011872343966,
+ 3.258266384852774,
+ 3.368883395896117,
+ 3.212863637874012,
+ 1.856084052053615,
+ 2.8494133123340486,
+ 1.0537473863751488,
+ 1.1011748620815691,
+ 1.3066035816802408,
+ 2.5526143902162364,
+ 3.396669734783293,
+ 1.9391168932760494,
+ 0.8306819661484934,
+ 3.0014690415597554,
+ 1.8775818253402554,
+ 0.7456174750318285,
+ 2.679431776143072,
+ 1.3797029876026845,
+ 1.0731301365181418,
+ 3.117794612454915,
+ 1.3564918752521802,
+ 1.6407750441731193,
+ 2.5737636487474815,
+ 2.8329577666186925,
+ 2.969435839121422,
+ 1.864733566891929,
+ 2.20092192586656,
+ 1.872892581990154,
+ 1.7043889451216478,
+ 2.0849701979936484,
+ 1.1810118768163949,
+ 3.294301808399455,
+ 0.9743654808997182,
+ 3.470192347424726,
+ 2.4509442847235774,
+ 3.0279001339152964,
+ 3.477822024417545,
+ 3.0839729278256245,
+ 2.901544435512654,
+ 3.2461831398793413,
+ 0.9765177687620732,
+ 3.11024465869721,
+ 3.1680791930398673,
+ 3.465001607719712,
+ 2.8781586784884143
+ ],
+ "N": [
+ 13,
+ 9,
+ 14,
+ 7,
+ 10,
+ 17,
+ 8,
+ 10,
+ 12,
+ 16,
+ 11,
+ 20,
+ 7,
+ 10,
+ 20,
+ 11,
+ 17,
+ 19,
+ 17,
+ 7,
+ 20,
+ 17,
+ 17,
+ 18,
+ 13,
+ 19,
+ 11,
+ 8,
+ 8,
+ 9,
+ 12,
+ 13,
+ 19,
+ 16,
+ 8,
+ 15,
+ 13,
+ 7,
+ 16,
+ 20,
+ 11,
+ 17,
+ 11,
+ 5,
+ 6,
+ 8,
+ 11,
+ 5,
+ 18,
+ 14
+ ],
+ "x": [
+ 11,
+ 2,
+ 9,
+ 6,
+ 6,
+ 13,
+ 7,
+ 9,
+ 4,
+ 13,
+ 4,
+ 18,
+ 1,
+ 1,
+ 10,
+ 5,
+ 14,
+ 18,
+ 10,
+ 1,
+ 9,
+ 6,
+ 7,
+ 8,
+ 4,
+ 15,
+ 10,
+ 2,
+ 2,
+ 8,
+ 1,
+ 1,
+ 11,
+ 14,
+ 5,
+ 4,
+ 4,
+ 1,
+ 6,
+ 8,
+ 6,
+ 6,
+ 9,
+ 4,
+ 5,
+ 1,
+ 8,
+ 4,
+ 1,
+ 10
+ ]
+}
\ No newline at end of file
diff --git a/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/test/fixtures/julia/runner.jl
new file mode 100644
index 00000000000..f78eb2f2393
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/test/fixtures/julia/runner.jl
@@ -0,0 +1,76 @@
+#!/usr/bin/env julia
+#
+# @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 Distributions: pmf, Boltzmann
+import JSON
+
+"""
+ gen( x, λ, N, name )
+
+Generate fixture data and write to file.
+
+# Arguments
+
+* `x`: input value of energy
+* `N`: ptotal number of energy states
+* `λ`: Inverse Temperature parameter
+* `name::AbstractString`: output filename
+
+# Examples
+
+``` julia
+julia> lambda = round.( ( rand( 100 ) ) .+ 20 );
+julia> N = round.( rand( 1000 ) .* 10 );
+julia> x = round.( rand( 1000 ) .* N );
+julia> gen( x, N, K, n, "data.json" );
+```
+"""
+function gen( x, lambda, N, name )
+ z = Array{Float64}( undef, length(x) );
+ for i in eachindex(x)
+ z[ i ] = pdf( Hypergeometric( lambda[i], N[i] ), x[i] );
+ end
+
+ # Store data to be written to file as a collection:
+ data = Dict([
+ ("x", x),
+ ("lambda", lambda),
+ ("N", N),
+ ("expected", z)
+ ]);
+
+ # Based on the script directory, create an output filepath:
+ filepath = joinpath( dir, name );
+
+ # Write the data to the output filepath as JSON:
+ outfile = open( filepath, "w" );
+ write( outfile, JSON.json(data) );
+ close( outfile );
+end
+
+# Get the filename:
+file = @__FILE__;
+
+# Extract the directory in which this file resides:
+dir = dirname( file );
+
+# Random:
+N = round.( ( rand( 100 ) ) .+ 50 );
+K = round.( rand( 1000 ) .* 10 );
+x = round.( rand( 1000 ) .* N );
+gen( x, N, K, n, "data.json" );
\ No newline at end of file
diff --git a/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/test/test.factory.js b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/test/test.factory.js
new file mode 100644
index 00000000000..9d6594bcec7
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/test/test.factory.js
@@ -0,0 +1,157 @@
+/**
+* @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 tape = require( 'tape' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var abs = require( '@stdlib/math/base/special/abs' );
+var PINF = require( '@stdlib/constants/float64/pinf' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+var factory = require( './../lib/factory.js' );
+
+
+// FIXTURES //
+
+var data = require( './fixtures/julia/data.json' );
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+ t.ok( true, __filename );
+ t.strictEqual( typeof factory, 'function', 'main export is a function' );
+ t.end();
+});
+
+tape( 'the function returns a function', function test( t ) {
+ var pmf = factory( 1.5, 10 );
+ t.equal( typeof pmf, 'function', 'returns a function' );
+ t.end();
+});
+
+tape( 'if provided `NaN` for any parameter, the created function returns `NaN`', function test( t ) {
+ var pmf;
+ var y;
+
+ pmf = factory( 1.5, 10 );
+ y = pmf( NaN );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ pmf = factory( NaN, 1.5 );
+ y = pmf( 0 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ pmf = factory( NaN, NaN );
+ y = pmf( 0 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ pmf = factory( NaN, NaN );
+ y = pmf( NaN );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ t.end();
+});
+
+tape( 'if provided valid parameters, the function returns a function which returns `0` when provided an integer `x` greater than `N`', function test( t ) {
+ var pmf;
+ var y;
+
+ pmf = factory( 1.5, 10 );
+
+ y = pmf( 12.0 );
+ t.equal( y, 0.0, 'returns 0' );
+
+ y = pmf( 11.0 );
+ t.equal( y, 0.0, 'returns 0' );
+
+ t.end();
+});
+
+tape( 'if provided an `N` which is not a nonnegative integer, the created function always returns `NaN`', function test( t ) {
+ var pmf;
+ var y;
+
+ pmf = factory( 2.5, 10.5 );
+
+ y = pmf( 2.0 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ y = pmf( 0.0 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ pmf = factory( 1.5, -10 );
+ y = pmf( 2.0 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ pmf = factory( 1.5, PINF );
+ y = pmf( 2.0 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ t.end();
+});
+
+tape( 'if provided a `λ` which is not a nonnegative integer, the created function always returns `NaN`', function test( t ) {
+ var pmf;
+ var y;
+
+ pmf = factory( -2.5, 10 );
+
+ y = pmf( 2.0 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ y = pmf( 0.0 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ pmf = factory( PINF, 10 );
+ y = pmf( 2.0 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ t.end();
+});
+
+tape( 'the created function evaluates the pmf for `x`', function test( t ) {
+ var expected;
+ var lambda;
+ var delta;
+ var pmf;
+ var tol;
+ var i;
+ var N;
+ var x;
+ var y;
+
+ expected = data.expected;
+ x = data.x;
+ N = data.N;
+ lambda = data.lambda;
+ for ( i = 0; i < x.length; i++ ) {
+ pmf = factory( lambda[i], N[i] );
+ y = pmf( x[i] );
+ if ( y === expected[i] ) {
+ t.equal( y, expected[i], 'x: '+x[i]+', lambda: '+lambda[i]+', N: '+N[i]+', y: '+y+', expected: '+expected[i] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 1040.0 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. lambda: '+lambda[i]+'. N: '+N[i]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' );
+ }
+ }
+ t.end();
+});
diff --git a/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/test/test.js b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/test/test.js
new file mode 100644
index 00000000000..bbf5e7fc9af
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/test/test.js
@@ -0,0 +1,38 @@
+/**
+* @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 tape = require( 'tape' );
+var pmf = require( './../lib' );
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+ t.ok( true, __filename );
+ t.strictEqual( typeof pmf, 'function', 'main export is a function' );
+ t.end();
+});
+
+tape( 'attached to the main export is a factory method for generating `pmf` functions', function test( t ) {
+ t.equal( typeof pmf.factory, 'function', 'exports a factory method' );
+ t.end();
+});
diff --git a/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/test/test.pmf.js b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/test/test.pmf.js
new file mode 100644
index 00000000000..e335047efb3
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/boltzmann/pmf/test/test.pmf.js
@@ -0,0 +1,122 @@
+/**
+* @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 tape = require( 'tape' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var abs = require( '@stdlib/math/base/special/abs' );
+var PINF = require( '@stdlib/constants/float64/pinf' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+var pmf = require( './../lib' );
+
+
+// FIXTURES //
+
+var data = require( './fixtures/julia/data.json' );
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+ t.ok( true, __filename );
+ t.strictEqual( typeof pmf, 'function', 'main export is a function' );
+ t.end();
+});
+
+tape( 'if provided `NaN` for any parameter, the function returns `NaN`', function test( t ) {
+ var y = pmf( NaN, 1.5, 10 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ y = pmf( 3, NaN, 10 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ y = pmf( 3, 1.5, NaN );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ t.end();
+});
+
+tape( 'if provided an integer `x` greater than `N`, the function returns `0` (provided all parameters are valid)', function test( t ) {
+ var y = pmf( 12, 1.2, 10 );
+ t.equal( y, 0.0, 'returns 0' );
+
+ y = pmf( 100, 1.2, 10 );
+ t.equal( y, 0.0, 'returns 0' );
+
+ t.end();
+});
+
+tape( 'if provided an `N` which is not a nonnegative integer, the function returns `NaN`', function test( t ) {
+ var y;
+
+ y = pmf( 2, 3.5, -10 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ y = pmf( 2, 2.5, 10.5 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ y = pmf( 2, 2.5, PINF );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ t.end();
+});
+
+tape( 'if provided a `λ` which is not a nonnegative integer, the function returns `NaN`', function test( t ) {
+ var y;
+
+ y = pmf( 2, -3.5, 10 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ y = pmf( 2, -2, 10 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ y = pmf( 0, PINF, 10 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ t.end();
+});
+
+tape( 'the function evaluates the pmf for `x`', function test( t ) {
+ var expected;
+ var lambda;
+ var delta;
+ var tol;
+ var x;
+ var N;
+ var y;
+ var i;
+
+ expected = data.expected;
+ x = data.x;
+ lambda = data.lambda;
+ N = data.N;
+ for ( i = 0; i < x.length; i++ ) {
+ y = pmf( x[i], lambda[i], N[i] );
+ if ( y === expected[i] ) {
+ t.equal( y, expected[i], 'x: '+x[i]+', lambda: '+lambda[i]+', N: '+N[i]+', y: '+y+', expected: '+expected[i] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 1040.0 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. lambda: '+lambda[i]+'. N: '+N[i]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' );
+ }
+ }
+ t.end();
+});