diff --git a/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/README.md b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/README.md
new file mode 100755
index 000000000000..7b0db871c044
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/README.md
@@ -0,0 +1,168 @@
+
+
+
+# Probability Density Function
+
+> [Skew normal][skew-normal-distribution] distribution probability density function (PDF).
+
+
+
+The [probability density function][pdf] (PDF) for a [skew normal][skew-normal-distribution] random variable is
+
+```math
+f(x;\mu,\sigma,\alpha)=\frac{2}{\sigma}\phi \left({\frac {x-\mu }{\sigma }}\right)\Phi \left(\alpha \left({\frac {x-\mu }{\sigma }}\right)\right)
+```
+
+where,
+
+> `ϕ` is the standard normal probability distribution function,
+> `Φ` is the standard normal cumulative distribution function,
+> `μ` is the mean,
+> `σ` is the standard deviation,
+> `α` is the skewness.
+
+
+
+
+
+
+
+## Usage
+
+```javascript
+var pdf = require( '@stdlib/stats/base/dists/skew-normal/pdf' );
+```
+
+#### pdf( x, mu, sigma, alpha )
+
+Evaluates the [probability density function][pdf] (PDF) for a [skew normal][skew-normal-distribution] distribution with parameters `mu` (mean), `sigma` (standard deviation), and `alpha` (skewness).
+
+```javascript
+var y = pdf( 2.0, 0.0, 1.0, 2.0 );
+// returns ~0.108
+
+y = pdf( -1.0, 4.0, 2.0, 0.0 );
+// returns ~0.009
+```
+
+If provided `NaN` as any argument, the function returns `NaN`.
+
+```javascript
+var y = pdf( NaN, 0.0, 1.0, 0.0 );
+// returns NaN
+
+y = pdf( 0.0, NaN, 1.0, 0.0 );
+// returns NaN
+
+y = pdf( 0.0, 0.0, NaN, 0.0 );
+// returns NaN
+
+y = pdf( 0.0, 0.0, 0.0, NaN );
+// returns NaN
+```
+
+If provided `sigma < 0`, the function returns `NaN`.
+
+```javascript
+var y = pdf( 2.0, 0.0, -1.0, 0.0 );
+// returns NaN
+```
+
+If provided `sigma = 0`, the function evaluates the [PDF][pdf] of a [degenerate distribution][degenerate-distribution] centered at `mu`.
+
+```javascript
+var y = pdf( 2.0, 8.0, 0.0, 0.0 );
+// returns 0.0
+
+y = pdf( 8.0, 8.0, 0.0, 0.0 );
+// returns Infinity
+```
+
+#### pdf.factory( mu, sigma, alpha )
+
+Partially apply `mu`, `sigma`, and `alpha` to create a reusable `function` for evaluating the PDF.
+
+```javascript
+var mypdf = pdf.factory( 10.0, 2.0, -1.0 );
+
+var y = mypdf( 10.0 );
+// returns ~0.199
+
+y = mypdf( 5.0 );
+// returns ~0.017
+```
+
+
+
+
+
+
+
+## Examples
+
+
+
+```javascript
+var randu = require( '@stdlib/random/base/randu' );
+var pdf = require( '@stdlib/stats/base/dists/skew-normal/pdf' );
+
+var alpha;
+var sigma;
+var mu;
+var x;
+var y;
+var i;
+
+for ( i = 0; i < 10; i++ ) {
+ x = randu() * 10.0;
+ mu = (randu() * 10.0) - 5.0;
+ sigma = randu() * 20.0;
+ alpha = (randu() * 40.0) - 20.0;
+ y = pdf( x, mu, sigma, alpha );
+ console.log( 'x: %d, µ: %d, σ: %d, α: %d, f(x;µ,σ,α): %d', x, mu, sigma, alpha, y );
+}
+```
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+[pdf]: https://en.wikipedia.org/wiki/Probability_density_function
+
+[skew-normal-distribution]: https://en.wikipedia.org/wiki/Skew_normal_distribution
+
+[degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution
+
+
+
+
diff --git a/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/benchmark/benchmark.js b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/benchmark/benchmark.js
new file mode 100755
index 000000000000..2090877c319e
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/benchmark/benchmark.js
@@ -0,0 +1,88 @@
+/**
+* @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 randu = require( '@stdlib/random/base/randu' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+var pkg = require( './../package.json' ).name;
+var pdf = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+ var alpha;
+ var sigma;
+ var mu;
+ var x;
+ var y;
+ var i;
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ x = ( randu()*200.0 ) - 100;
+ mu = ( randu()*100.0 ) - 50.0;
+ sigma = ( randu()*20.0 ) + EPS;
+ alpha = ( randu()*40.0 ) - 20.0;
+ y = pdf( x, mu, sigma, alpha );
+ 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 mypdf;
+ var alpha;
+ var sigma;
+ var mu;
+ var x;
+ var y;
+ var i;
+
+ mu = 0.0;
+ sigma = 1.5;
+ alpha = 0.5;
+ mypdf = pdf.factory( mu, sigma, alpha);
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ x = ( randu()*6.0 ) - 3.0;
+ y = mypdf( 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/skew-normal/pdf/benchmark/r/DESCRIPTION b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/benchmark/r/DESCRIPTION
new file mode 100755
index 000000000000..54c45ca4a7b4
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/benchmark/r/DESCRIPTION
@@ -0,0 +1,10 @@
+Package: sn-benchmarks
+Title: Benchmarks
+Version: 0.0.0
+Authors@R: person("stdlib", "js", role = c("aut","cre"))
+Description: Benchmarks.
+Depends: R (>=3.4.0)
+Imports:
+ microbenchmark
+ sn
+LazyData: true
diff --git a/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/benchmark/r/benchmark.R b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/benchmark/r/benchmark.R
new file mode 100755
index 000000000000..c1ac19b999e0
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/benchmark/r/benchmark.R
@@ -0,0 +1,114 @@
+#!/usr/bin/env Rscript
+#
+# @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.
+
+# Set the precision to 16 digits:
+options( digits = 16L );
+
+#' Run benchmarks.
+#'
+#' @examples
+#' main();
+main <- function() {
+ # Define benchmark parameters:
+ name <- 'dist-skew-normal-pdf';
+ iterations <- 1000000L;
+ repeats <- 3L;
+
+ #' Print the TAP version.
+ #'
+ #' @examples
+ #' print_version();
+ print_version <- function() {
+ cat( 'TAP version 13\n' );
+ }
+
+ #' Print the TAP summary.
+ #'
+ #' @param total Total number of tests.
+ #' @param passing Total number of passing tests.
+ #'
+ #' @examples
+ #' print_summary( 3, 3 );
+ print_summary <- function( total, passing ) {
+ cat( '#\n' );
+ cat( paste0( '1..', total, '\n' ) ); # TAP plan
+ cat( paste0( '# total ', total, '\n' ) );
+ cat( paste0( '# pass ', passing, '\n' ) );
+ cat( '#\n' );
+ cat( '# ok\n' );
+ }
+
+ #' Print benchmark results.
+ #'
+ #' @param iterations Number of iterations.
+ #' @param elapsed Elapsed time in seconds.
+ #'
+ #' @examples
+ #' print_results( 10000L, 0.131009101868 );
+ print_results <- function( iterations, elapsed ) {
+ rate <- iterations / elapsed;
+ cat( ' ---\n' );
+ cat( paste0( ' iterations: ', iterations, '\n' ) );
+ cat( paste0( ' elapsed: ', elapsed, '\n' ) );
+ cat( paste0( ' rate: ', rate, '\n' ) );
+ cat( ' ...\n' );
+ }
+
+ #' Run a benchmark.
+ #'
+ #' ## Notes
+ #'
+ #' * We compute and return a total "elapsed" time, rather than the minimum
+ #' evaluation time, to match benchmark results in other languages (e.g.,
+ #' Python).
+ #'
+ #'
+ #' @param iterations Number of Iterations.
+ #' @return Elapsed time in seconds.
+ #'
+ #' @examples
+ #' elapsed <- benchmark( 10000L );
+ benchmark <- function( iterations ) {
+ # Run the benchmarks:
+ results <- microbenchmark::microbenchmark(sn::dsn(
+ runif( 1.0, -100.0, 100.0 ),
+ runif( 1.0, -50.0, 50.0 ),
+ runif( 1.0, .Machine$double.eps, 20.0 ), # nolint
+ runif( 1.0, -20.0, 20.0 )
+ ), times = iterations );
+
+ # Sum all the raw timing results to get a total "elapsed" time:
+ elapsed <- sum( results$time ); # nolint
+
+ # Convert the elapsed time from nanoseconds to seconds:
+ elapsed <- elapsed / 1.0e9;
+
+ return( elapsed );
+ }
+
+ print_version();
+ for ( i in 1L:repeats ) {
+ cat( paste0( '# r::', name, '\n' ) );
+ elapsed <- benchmark( iterations );
+ print_results( iterations, elapsed );
+ cat( paste0( 'ok ', i, ' benchmark finished', '\n' ) );
+ }
+ print_summary( repeats, repeats );
+}
+
+main();
diff --git a/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/docs/repl.txt b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/docs/repl.txt
new file mode 100755
index 000000000000..57271cec3317
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/docs/repl.txt
@@ -0,0 +1,84 @@
+
+{{alias}}( x, μ, σ, α )
+ Evaluates the probability density function (PDF) for a skew normal
+ distribution with mean `μ`, standard deviation `σ`, and skewness `α`
+ at a value `x`.
+
+ If provided `NaN` as any argument, the function returns `NaN`.
+
+ If provided `σ < 0`, the function returns `NaN`.
+
+ Parameters
+ ----------
+ x: number
+ Input value.
+
+ μ: number
+ Location parameter (Mean).
+
+ σ: number
+ Scale parameter (Standard deviation).
+
+ α: number
+ Shape parameter (Skewness).
+
+ Returns
+ -------
+ out: number
+ Evaluated PDF.
+
+ Examples
+ --------
+ > var y = {{alias}}( 2.0, 0.0, 1.0, 2.0 )
+ ~0.108
+ > y = {{alias}}( -1.0, 4.0, 2.0, 0.0 )
+ ~0.009
+ > y = {{alias}}( NaN, 0.0, 1.0, 0.0 )
+ NaN
+ > y = {{alias}}( 0.0, NaN, 1.0, 0.0 )
+ NaN
+ > y = {{alias}}( 0.0, 0.0, NaN, 0.0 )
+ NaN
+ > y = {{alias}}( 0.0, 0.0, 1.0, NaN )
+ NaN
+
+ // Negative standard deviation:
+ > y = {{alias}}( 2.0, 0.0, -1.0, 0.0 )
+ NaN
+
+ // Degenerate distribution centered at `μ` when `σ = 0.0`:
+ > y = {{alias}}( 2.0, 8.0, 0.0, 1.0 )
+ 0.0
+ > y = {{alias}}( 8.0, 8.0, 0.0, 1.0 )
+ Infinity
+
+
+{{alias}}.factory( μ, σ, α )
+ Returns a function for evaluating the probability density function (PDF)
+ of a skew normal distribution with mean `μ`, standard deviation `σ`, and
+ skewness `α`.
+
+ Parameters
+ ----------
+ μ: number
+ Location parameter (Mean).
+
+ σ: number
+ Scale parameter (Standard deviation).
+
+ α: number
+ Shape parameter (Skewness).
+
+ Returns
+ -------
+ pdf: Function
+ Probability density function (PDF).
+
+ Examples
+ --------
+ > var myPDF = {{alias}}.factory( 10.0, 2.0, -1.0 );
+ > var y = myPDF( 10.0 )
+ ~0.199
+
+ See Also
+ --------
diff --git a/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/examples/index.js b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/examples/index.js
new file mode 100755
index 000000000000..c65ccae040fd
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/examples/index.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';
+
+var randu = require( '@stdlib/random/base/randu' );
+var pdf = require( './../lib' );
+
+var alpha;
+var sigma;
+var mu;
+var x;
+var y;
+var i;
+
+for ( i = 0; i < 10; i++ ) {
+ x = randu() * 10.0;
+ mu = (randu() * 10.0) - 5.0;
+ sigma = randu() * 20.0;
+ alpha = (randu() * 20.0) - 10.0;
+ y = pdf( x, mu, sigma, alpha );
+ console.log( 'x: %d, µ: %d, σ: %d, α: %d,f(x;µ,σ,α): %d', x.toFixed( 4 ), mu.toFixed( 4 ), sigma.toFixed( 4 ), alpha.toFixed(4), y.toFixed( 4 ) );
+}
diff --git a/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/lib/factory.js b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/lib/factory.js
new file mode 100755
index 000000000000..dd0fb9d1f058
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/lib/factory.js
@@ -0,0 +1,82 @@
+/**
+* @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 constantFunction = require( '@stdlib/utils/constant-function' );
+var normalPdf = require( '@stdlib/stats/base/dists/normal/pdf' );
+var normalCdf = require( '@stdlib/stats/base/dists/normal/cdf' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+
+
+// MAIN //
+
+/**
+* Returns a function for evaluating the probability density function (PDF) for a skewed normal distribution.
+*
+* @param {number} mu - mean
+* @param {NonNegativeNumber} sigma - standard deviation
+* @param {number} alpha - skewness
+* @returns {Function} function to evaluate the probability density function
+*
+* @example
+* var pdf = factory( 10.0, 2.0, -1.0 );
+* var y = pdf( 10.0 );
+* // returns ~0.199
+*
+* y = pdf( 5.0 );
+* // returns ~0.017
+*/
+function factory( mu, sigma, alpha ) {
+ var pdfFactory;
+ var cdfFactory;
+ pdfFactory = normalPdf.factory( mu, sigma );
+ if ( alpha === 0.0 ) {
+ return pdfFactory;
+ }
+ if ( isnan(alpha) ) {
+ return constantFunction( NaN );
+ }
+ cdfFactory = normalCdf.factory( alpha * mu, sigma );
+ return pdf;
+
+ /**
+ * Evaluates the probability density function (PDF) for a skewed normal distribution.
+ *
+ * @private
+ * @param {number} x - input value
+ * @returns {number} evaluated probability density function
+ *
+ * @example
+ * var y = pdf( -3.14 );
+ * // returns
+ */
+ function pdf( x ) {
+ if ( isnan( x ) ) {
+ return NaN;
+ }
+ return 2 * pdfFactory( x ) * cdfFactory( alpha * x );
+ }
+}
+
+
+// EXPORTS //
+
+module.exports = factory;
diff --git a/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/lib/index.js b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/lib/index.js
new file mode 100755
index 000000000000..01261d6ff6cb
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/lib/index.js
@@ -0,0 +1,51 @@
+/**
+* @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';
+
+/**
+* Skewed normal distribution probability density function (PDF).
+*
+* @module @stdlib/stats/base/dists/skew-normal/pdf
+*
+* @example
+* var pdf = require( '@stdlib/stats/base/dists/skew-normal/pdf' );
+*
+* var y = pdf( 2.0, 0.0, 1.0, 2.0 );
+* // returns ~0.108
+*
+* var myPDF = pdf.factory( 10.0, 2.0, -1.0 );
+* y = myPDF( 10.0 );
+* // returns ~0.199
+*/
+
+// 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/skew-normal/pdf/lib/main.js b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/lib/main.js
new file mode 100755
index 000000000000..2ac10538c319
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/lib/main.js
@@ -0,0 +1,94 @@
+/**
+* @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 normalPdf = require( '@stdlib/stats/base/dists/normal/pdf' );
+var normalCdf = require( '@stdlib/stats/base/dists/normal/cdf' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+
+
+// MAIN //
+
+/**
+* Evaluates the probability density function (PDF) for a skewed normal distribution with mean `mu`, standard deviation `sigma`, and skewness `alpha` at a value `x`.
+*
+* @param {number} x - input value
+* @param {number} mu - mean
+* @param {NonNegativeNumber} sigma - standard deviation
+* @param {number} alpha - skewness
+* @returns {number} evaluated probability density function
+*
+* @example
+* var y = pdf( 2.0, 0.0, 1.0, 2.0 );
+* // returns ~0.108
+*
+* @example
+* var y = pdf( -1.0, 4.0, 2.0, 0.0 );
+* // returns ~0.009
+*
+* @example
+* var y = pdf( NaN, 0.0, 1.0, 0.0 );
+* // returns NaN
+*
+* @example
+* var y = pdf( 0.0, NaN, 1.0, 0.0 );
+* // returns NaN
+*
+* @example
+* var y = pdf( 0.0, 0.0, NaN, 0.0 );
+* // returns NaN
+*
+* @example
+* var y = pdf( 0.0, 0.0, 1.0, NaN );
+* // returns NaN
+*
+* @example
+* // Negative standard deviation:
+* var y = pdf( 2.0, 0.0, -1.0, 0.0 );
+* // returns NaN
+*
+* @example
+* // Degenerate distribution centered at `μ` when `σ = 0.0`:
+* var y = pdf( 2.0, 8.0, 0.0, 1.0 );
+* // returns 0.0
+*
+* @example
+* var y = pdf( 8.0, 8.0, 0.0, 1.0 );
+* // returns Infinity
+*/
+function pdf( x, mu, sigma, alpha ) {
+ var pdf;
+ var cdf;
+ pdf = normalPdf( x, mu, sigma );
+ if ( alpha === 0.0 ) {
+ return pdf;
+ }
+ if ( isnan(alpha) ) {
+ return NaN;
+ }
+ cdf = normalCdf( alpha * x, alpha * mu, sigma );
+ return 2 * pdf * cdf;
+}
+
+
+// EXPORTS //
+
+module.exports = pdf;
diff --git a/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/package.json b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/package.json
new file mode 100755
index 000000000000..4e36aa23c827
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/package.json
@@ -0,0 +1,62 @@
+{
+ "name": "@stdlib/stats/base/dists/skew-normal/pdf",
+ "version": "0.0.0",
+ "description": "Skew normal distribution probability density function (PDF).",
+ "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": {
+ "lib": "./lib"
+ },
+ "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",
+ "continuous",
+ "probability",
+ "pdf",
+ "gaussian",
+ "normal",
+ "skew",
+ "bell-shape",
+ "univariate"
+ ]
+}
diff --git a/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/test/fixtures/r/DESCRIPTION b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/test/fixtures/r/DESCRIPTION
new file mode 100755
index 000000000000..747de03e3668
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/test/fixtures/r/DESCRIPTION
@@ -0,0 +1,10 @@
+Package: skew-normal-pdf-test-fixtures
+Title: Test Fixtures
+Version: 0.0.0
+Authors@R: person("stdlib", "js", role = c("aut","cre"))
+Description: Generates test fixtures.
+Depends: R (>=3.4.0)
+Imports:
+ jsonlite
+ sn
+LazyData: true
diff --git a/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/test/fixtures/r/data.json b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/test/fixtures/r/data.json
new file mode 100755
index 000000000000..3c137b937f46
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/test/fixtures/r/data.json
@@ -0,0 +1 @@
+{"mu":[-6.6966966966966961,-2.6126126126126126,5.015015015015015,-5.3753753753753752,4.5345345345345347,4.6346346346346348,1.1111111111111107,-6.3963963963963959,0.75075075075075048,-8.7387387387387392,-8.378378378378379,1.3113113113113108,7.1771771771771782,1.3513513513513509,0.7707707707707705,3.6736736736736741,-4.4144144144144146,-1.1111111111111107,-9.6196196196196198,-2.5325325325325325,-0.51051051051051033,-3.4534534534534531,-5.4554554554554553,-9.3993993993993996,-0.9309309309309306,8.6786786786786791,-3.0130130130130128,-2.4124124124124124,8.0380380380380387,2.8528528528528536,8.7787787787787792,7.3373373373373383,-5.4354354354354353,7.9379379379379387,-1.2512512512512508,-5.3153153153153152,2.3123123123123115,-7.9579579579579578,1.4514514514514509,-7.6176176176176176,-4.5345345345345347,-4.3943943943943946,-8.0180180180180187,-7.9779779779779778,7.9979979979979987,6.5965965965965978,-3.8738738738738743,-3.8538538538538543,2.1321321321321314,-7.7177177177177176,4.4944944944944947,1.9319319319319312,9.7797797797797799,-3.333333333333333,8.5985985985985991,9.6596596596596598,0.67067067067067043,0.85085085085085055,-5.6956956956956954,3.2332332332332339,-2.7927927927927927,-9.7597597597597598,-8.9589589589589593,5.035035035035035,6.6966966966966979,7.2172172172172182,2.4524524524524516,-0.41041041041041026,0.63063063063063041,8.8188188188188192,-5.2352352352352352,-1.591591591591591,-4.2942942942942945,0.13013013013013008,7.8578578578578586,-5.7757757757757755,-3.6736736736736741,-3.1731731731731729,-1.8518518518518512,5.8158158158158155,7.5975975975975985,9.97997997997998,-8.1981981981981988,4.1941941941941945,4.9149149149149149,3.493493493493494,-8.0980980980980988,4.0340340340340344,4.6546546546546548,-5.055055055055055,-5.1751751751751751,2.8128128128128118,9.0790790790790794,-7.7977977977977977,4.934934934934935,-6.3363363363363359,-7.4374374374374375,4.0540540540540544,-4.1741741741741745,8.2982982982982989,2.8928928928928936,9.4194194194194196,0.55055055055055035,2.9729729729729737,0.11011011011011007,0.33033033033033021,-8.9789789789789793,3.2732732732732739,-8.0580580580580587,6.876876876876878,-8.458458458458459,3.3133133133133139,8.7387387387387392,6.3363363363363376,9.8398398398398399,-9.1191191191191194,-5.2552552552552552,4.2742742742742745,6.1961961961961975,-9.8198198198198199,-1.1511511511511507,-6.0560560560560557,3.1731731731731738,-2.8128128128128127,-7.1171171171171173,5.5155155155155153,6.6166166166166178,0.53053053053053034,-9.97997997997998,1.0110110110110107,4.5545545545545547,8.6986986986986992,-6.556556556556556,-2.5525525525525525,0.69069069069069045,0.39039039039039025,-1.1911911911911908,-6.536536536536536,5.1551551551551551,4.3743743743743746,-0.67067067067067043,1.9119119119119112,-3.4734734734734731,6.856856856856858,0.21021021021021014,1.8918918918918912,-2.2522522522522523,-5.1951951951951951,-3.4334334334334331,-0.17017017017017011,2.6326326326326317,6.4564564564564577,-3.7337337337337342,-4.3743743743743746,8.6186186186186191,-7.7577577577577577,-5.8358358358358355,-4.7547547547547548,6.916916916916918,-5.6356356356356354,-1.6516516516516511,-3.5535535535535532,8.2382382382382389,0.4704704704704703,-3.3533533533533531,-5.5155155155155153,9.7197197197197198,4.8148148148148149,7.7777777777777786,8.9989989989989994,-0.59059059059059038,-9.1591591591591595,2.8328328328328336,-0.55055055055055035,-1.611611611611611,6.6566566566566578,-0.95095095095095061,-8.9189189189189193,8.2782782782782789,9.3393393393393396,9.1191191191191194,9.2992992992992995,0.1501501501501501,-9.95995995995996,6.2162162162162176,5.3153153153153152,-0.45045045045045029,-1.2112112112112108,2.1721721721721714,0.010010010010010006,-9.4394394394394396,7.0170170170170181,3.0930930930930938,-2.5125125125125125,-6.1361361361361357,1.591591591591591,-6.2962962962962958,-6.3163163163163158,-3.253253253253253,4.3943943943943946,-8.6386386386386391,5.3953953953953953,6.1161161161161175,4.4344344344344346,-2.6526526526526526,3.0330330330330337,5.6556556556556554,0.25025025025025016,-6.8768768768768771,1.8318318318318312,-1.531531531531531,9.7997997997997999,-9.4594594594594597,3.0730730730730738,5.5555555555555554,5.9759759759759756,1.3713713713713709,-2.7527527527527527,-3.213213213213213,4.7347347347347348,5.7157157157157155,7.0970970970970981,-9.7197197197197198,-6.1761761761761758,8.2182182182182189,-3.1331331331331329,7.4174174174174183,8.8788788788788793,5.1951951951951951,3.1531531531531538,-4.6946946946946948,-9.7997997997997999,-0.4704704704704703,7.4574574574574584,-6.516516516516516,9.9199199199199199,8.6586586586586591,8.3583583583583589,-2.0520520520520522,-0.53053053053053034,-3.3733733733733731,7.6576576576576585,9.0590590590590594,9.3993993993993996,5.1751751751751751,4.4744744744744747,0.49049049049049032,-3.0530530530530529,4.994994994994995,2.1921921921921914,-7.5775775775775776,-0.39039039039039025,-0.63063063063063041,-0.43043043043043028,-8.8788788788788793,-8.1181181181181188,-2.3323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diff --git a/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/test/fixtures/r/runner.R b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/test/fixtures/r/runner.R
new file mode 100755
index 000000000000..58320580864a
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/test/fixtures/r/runner.R
@@ -0,0 +1,99 @@
+#!/usr/bin/env Rscript
+#
+# @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.
+
+# Set the precision to 16 digits:
+options( digits = 16L );
+
+# Set the PRNG seed:
+set.seed( 200L );
+
+#' Generate test fixtures.
+#'
+#' @examples
+#' main();
+main <- function() {
+ #' Get the script filepath.
+ #'
+ #' @return The absolute path of this script
+ #'
+ #' @examples
+ #' filepath <- get_script_path();
+ get_script_path <- function() {
+ args <- commandArgs( trailingOnly = FALSE );
+ needle <- '--file=';
+ match <- grep( needle, args );
+ if ( length( match ) > 0L ) {
+ # Rscript:
+ filepath <- sub( needle, '', args[match] );
+ } else {
+ ls_vars <- ls( sys.frames()[[1L]] )
+ if ( 'fileName' %in% ls_vars ) {
+ # Source'd via RStudio:
+ filepath <- sys.frames()[[1L]]$fileName; # nolint
+ } else {
+ # Source'd via R console:
+ filepath <- sys.frames()[[1L]]$ofile; # nolint
+ }
+ }
+ return( normalizePath( filepath ) );
+ }
+
+ #' Convert a data structure to JSON.
+ #'
+ #' @param x A data structure to convert
+ #' @return JSON blob
+ #'
+ #' @examples
+ #' x <- seq( -6.5, 25, 0.5 );
+ #' json <- to_json( x );
+ to_json <- function( x ) {
+ return( jsonlite::toJSON( x, digits = 16L, auto_unbox = TRUE ) );
+ }
+
+ #' Generate an output absolute filepath based on the script directory.
+ #'
+ #' @param name An output filename
+ #' @return An absolute filepath
+ #'
+ #' @examples
+ #' filepath <- get_filepath( "data.json" );
+ get_filepath <- function( name ) {
+ return( paste( source_dir, '/', name, sep = '' ) );
+ }
+
+ # Get the directory of this script:
+ source_dir <- dirname( get_script_path() );
+
+ # Generate test fixture data:
+ mu <- sample( seq( -10.0, 10.0, length.out = 1000L ) );
+ sigma <- sample( seq( 0.1, 100.0, length.out = 1000L ) );
+ alpha <- sample( seq( -20.0, 20.0, length.out = 1000L ) );
+ x <- sample( seq( -100.0, 100.0, length.out = 1000L ) );
+ y <- sn::dsn( x, mu, sigma, alpha );
+
+ data <- list( mu = mu, sigma = sigma, alpha = alpha, x = x, expected = y );
+
+ # Convert fixture data to JSON:
+ data <- to_json( data );
+
+ # Write the data to file...
+ filepath <- get_filepath( 'data.json' );
+ write( data, filepath );
+}
+
+main();
diff --git a/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/test/test.factory.js b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/test/test.factory.js
new file mode 100755
index 000000000000..7fb1747298e9
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/test/test.factory.js
@@ -0,0 +1,200 @@
+/**
+* @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 NINF = require( '@stdlib/constants/float64/ninf' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+var factory = require( './../lib/factory.js' );
+
+
+// FIXTURES //
+
+var data = require( './fixtures/r/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 pdf = factory( 0.0, 1.0 );
+ t.equal( typeof pdf, 'function', 'returns a function' );
+ t.end();
+});
+
+tape( 'if provided `NaN` for any parameter, the created function returns `NaN`', function test( t ) {
+ var pdf;
+ var y;
+
+ pdf = factory( 0.0, 1.0, 0.0 );
+ y = pdf( NaN );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ pdf = factory( NaN, 1.0, 0.0 );
+ y = pdf( 0.0 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ pdf = factory( 1.0, NaN, 0.0 );
+ y = pdf( 0.0 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ pdf = factory(0.0, 0.0, NaN );
+ y = pdf( 0.0 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ pdf = factory( NaN, NaN, NaN );
+ y = pdf( 0.0 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ pdf = factory( NaN, NaN, NaN);
+ y = pdf( NaN );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ t.end();
+});
+
+tape( 'if provided a finite `mu`, `sigma`, and `alpha`, the function returns a function which returns `0` when provided `+infinity` for `x`', function test( t ) {
+ var pdf;
+ var y;
+
+ pdf = factory( 0.0, 1.0, 10.0 );
+ y = pdf( PINF );
+ t.equal( y, 0.0, 'returns 0' );
+
+ t.end();
+});
+
+tape( 'if provided a finite `mu`, `sigma`, and `alpha`, the function returns a function which returns `0` when provided `-infinity` for `x`', function test( t ) {
+ var pdf;
+ var y;
+
+ pdf = factory( 0.0, 1.0, 10.0 );
+ y = pdf( NINF );
+ t.equal( y, 0.0, 'returns 0' );
+
+ t.end();
+});
+
+tape( 'if provided a negative `sigma`, the created function always returns `NaN`', function test( t ) {
+ var pdf;
+ var y;
+
+ pdf = factory( 0.0, -1.0, 0.0);
+
+ y = pdf( 2.0 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ y = pdf( 0.0 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ pdf = factory( 0.0, NINF, 0.0 );
+ y = pdf( 2.0 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ pdf = factory( PINF, NINF, 0.0 );
+ y = pdf( 2.0 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ pdf = factory( NINF, NINF, 0.0 );
+ y = pdf( 2.0 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ pdf = factory( NaN, NINF, 0.0 );
+ y = pdf( 2.0 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ pdf = factory( 0.0, NINF, PINF );
+ y = pdf( 2.0 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ pdf = factory( 0.0, NINF, NINF );
+ y = pdf( 2.0 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ pdf = factory( 0.0, NINF, NaN );
+ y = pdf( 2.0 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ t.end();
+});
+
+tape( 'if `sigma` equals `0`, the created function evaluates a degenerate distribution centered at `mu`', function test( t ) {
+ var pdf;
+ var y;
+
+ pdf = factory( 2.0, 0.0, 1.0 );
+
+ y = pdf( 2.0 );
+ t.equal( y, PINF, 'returns +infinity for x equal to mu' );
+
+ y = pdf( 1.0 );
+ t.equal( y, 0.0, 'returns 0' );
+
+ y = pdf( PINF );
+ t.equal( y, 0.0, 'returns 0' );
+
+ y = pdf( NINF );
+ t.equal( y, 0.0, 'returns 0' );
+
+ y = pdf( NaN );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ t.end();
+});
+
+tape( 'the created function evaluates the pdf for `x` given parameters `mu` and `sigma`', function test( t ) {
+ var expected;
+ var alpha;
+ var delta;
+ var sigma;
+ var pdf;
+ var tol;
+ var mu;
+ var x;
+ var y;
+ var i;
+
+ expected = data.expected;
+ x = data.x;
+ mu = data.mu;
+ sigma = data.sigma;
+ alpha = data.alpha;
+ for ( i = 0; i < x.length; i++ ) {
+ pdf = factory( mu[i], sigma[i], alpha[i]);
+ y = pdf( x[i] );
+ if ( y === expected[i] ) {
+ t.equal( y, expected[i], 'x: '+x[i]+', mu: '+mu[i]+', sigma: '+sigma[i]+', alpha: '+alpha[i]+', y: '+y+', expected: '+expected[i] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 5300.0 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: '+x[ i ]+'. mu: '+mu[i]+'. sigma: '+sigma[i]+'. alpha: '+alpha[i]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' );
+ }
+ }
+ t.end();
+});
diff --git a/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/test/test.js b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/test/test.js
new file mode 100755
index 000000000000..7d948ef6f138
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/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 pdf = require( './../lib' );
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+ t.ok( true, __filename );
+ t.strictEqual( typeof pdf, 'function', 'main export is a function' );
+ t.end();
+});
+
+tape( 'attached to the main export is a factory method for generating `pdf` functions', function test( t ) {
+ t.equal( typeof pdf.factory, 'function', 'exports a factory method' );
+ t.end();
+});
diff --git a/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/test/test.pdf.js b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/test/test.pdf.js
new file mode 100755
index 000000000000..7443a0615e76
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/test/test.pdf.js
@@ -0,0 +1,177 @@
+/**
+* @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 NINF = require( '@stdlib/constants/float64/ninf' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+var pdf = require( './../lib' );
+
+
+// FIXTURES //
+
+var data = require( './fixtures/r/data.json' );
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+ t.ok( true, __filename );
+ t.strictEqual( typeof pdf, 'function', 'main export is a function' );
+ t.end();
+});
+
+tape( 'if provided `NaN` for any parameter, the function returns `NaN`', function test( t ) {
+ var y;
+
+ y = pdf( NaN, 0.0, 1.0, 0.0 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ y = pdf( 0.0, NaN, 1.0, 0.0 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ y = pdf( 0.0, 1.0, NaN, 0.0 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ y = pdf( 0.0, 1.0, 0.0, NaN );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ y = pdf( NaN, NaN, 1.0, 0.0 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ y = pdf( NaN, 1.0, NaN, 0.0 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ y = pdf( NaN, 1.0, 0.0, NaN );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ y = pdf( 1.0, NaN, 0.0, NaN );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ y = pdf( 0.0, 0.0, NaN, NaN );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ y = pdf( NaN, NaN, NaN, 0.0 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ y = pdf( NaN, NaN, 0.0, NaN );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ y = pdf( NaN, 0.0, NaN, NaN );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ y = pdf( 0.0, NaN, NaN, NaN );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ y = pdf( NaN, NaN, NaN, NaN );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ t.end();
+});
+
+tape( 'if provided `+infinity` for `x` and a finite `mu`, `sigma`, and `alpha`, the function returns `0`', function test( t ) {
+ var y = pdf( PINF, 0.0, 1.0, 0.0 );
+ t.equal( y, 0.0, 'returns 0' );
+ t.end();
+});
+
+tape( 'if provided `-infinity` for `x` and a finite `mu`, `sigma`, and `alpha`, the function returns `0`', function test( t ) {
+ var y = pdf( NINF, 0.0, 1.0, 0.0 );
+ t.equal( y, 0.0, 'returns 0' );
+ t.end();
+});
+
+tape( 'if provided a negative `sigma`, the function always returns `NaN`', function test( t ) {
+ var y;
+
+ y = pdf( 2.0, 0.0, -1.0, 0.1 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ y = pdf( 0.0, 0.0, -1.0, 0.1 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ y = pdf( 2.0, 0.0, NINF, 0.1 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ y = pdf( 2.0, PINF, NINF, 0.1 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ y = pdf( 2.0, NINF, NINF, 0.1 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ y = pdf( 2.0, NaN, NINF, 0.1 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ t.end();
+});
+
+tape( 'if provided `sigma` equals `0`, the function evaluates a degenerate distribution centered at `mu`', function test( t ) {
+ var y;
+
+ y = pdf( 2.0, 2.0, 0.0, 0.1 );
+ t.equal( y, PINF, 'returns +infinity for x equal to mu' );
+
+ y = pdf( 1.0, 2.0, 0.0, 0.1 );
+ t.equal( y, 0.0, 'returns 0' );
+
+ y = pdf( PINF, 2.0, 0.0, 0.1 );
+ t.equal( y, 0.0, 'returns 0' );
+
+ y = pdf( NINF, 2.0, 0.0, 0.1 );
+ t.equal( y, 0.0, 'returns 0' );
+
+ y = pdf( NaN, 2.0, 0.0, 0.1 );
+ t.equal( isnan( y ), true, 'returns NaN' );
+
+ t.end();
+});
+
+tape( 'the function evaluates the pdf for `x` given parameters `mu`, `sigma`, and `alpha`', function test( t ) {
+ var expected;
+ var alpha;
+ var delta;
+ var sigma;
+ var tol;
+ var mu;
+ var x;
+ var y;
+ var i;
+
+ expected = data.expected;
+ x = data.x;
+ mu = data.mu;
+ sigma = data.sigma;
+ alpha = data.alpha;
+ for ( i = 0; i < x.length; i++ ) {
+ y = pdf( x[i], mu[i], sigma[i], alpha[i]);
+ if ( y === expected[i] ) {
+ t.equal( y, expected[i], 'x: '+x[i]+', mu:'+mu[i]+', sigma: '+sigma[i]+', alpha: '+alpha[i]+', y: '+y+', expected: '+expected[i] );
+ } else {
+ delta = abs( y - expected[ i ] );
+ tol = 5300.0 * EPS * abs( expected[ i ] );
+ t.ok( delta <= tol, 'within tolerance. x: '+x[ i ]+'. mu: '+mu[i]+'. sigma: '+sigma[i]+'. alpha: '+alpha[i]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' );
+ }
+ }
+ t.end();
+});