feat: add support for skew normal distribution PDF

lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/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 Density Function
+
+> [Skew normal][skew-normal-distribution] distribution probability density function (PDF).
+
+<section class="intro">
+
+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.
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## 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
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```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 );
+}
+```
+
+</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">
+
+[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
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/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 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();
+});

lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/benchmark/r/DESCRIPTION

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+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

lib/node_modules/@stdlib/stats/base/dists/skew-normal/pdf/benchmark/r/benchmark.R

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+#!/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();