math: Updated atanh implementation based on FreeBSD for improved accuracy and efficiency

lib/node_modules/@stdlib/math/base/special/atanh/lib/atanh.js

@@ -0,0 +1,86 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2018 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 isnan = require( '@stdlib/math-base-assert-is-nan' );
+var log1p = require( '@stdlib/math-base-special-log1p' );
+var PINF = require( '@stdlib/constants-float64-pinf' );
+var NINF = require( '@stdlib/constants-float64-ninf' );
+
+
+// MAIN //
+
+/**
+* Computes the hyperbolic arctangent of a number.
+*
+* @param {number} x - input value
+* @returns {number} hyperbolic arctangent
+*
+* @example
+* var v = atanh( 0.5 );
+* // returns ~0.549
+*
+* @example
+* var v = atanh( 0.0 );
+* // returns 0.0
+*
+* @example
+* var v = atanh( -0.0 );
+* // returns -0.0
+*
+* @example
+* var v = atanh( 1.0 );
+* // returns Infinity
+*
+* @example
+* var v = atanh( -1.0 );
+* // returns -Infinity
+*
+* @example
+* var v = atanh( 2.0 );
+* // returns NaN
+*
+* @example
+* var v = atanh( NaN );
+* // returns NaN
+*/
+function atanh( x ) {
+	var ax;
+	if ( isnan( x ) || x < -1.0 || x > 1.0 ) {
+		return NaN;
+	}
+	if ( x === 1.0 ) {
+		return PINF;
+	}
+	if ( x === -1.0 ) {
+		return NINF;
+	}
+	ax = ( x < 0.0 ) ? -x : x;
+	if ( ax < 0.5 ) {
+		return x + ( x * x * x / 3.0 );
+	}
+	return 0.5 * log1p( ( 2.0 * x ) / ( 1.0 - x ) );
+}
+
+
+// EXPORTS //
+
+module.exports = atanh;

lib/node_modules/@stdlib/stats/base/dists/hypergeometric/README.md

@@ -108,7 +108,80 @@ var y = dist.cdf( 0.5 );
 var objectKeys = require( '@stdlib/utils/keys' );
 var hypergeometric = require( '@stdlib/stats/base/dists/hypergeometric' );
 
+
 console.log( objectKeys( hypergeometric ) );
+
+// Example 1: Basic distribution properties
+var N1 = 50; // population size
+var K1 = 20; // number of successes in population
+var n1 = 10; // number of draws
+
+console.log( '\nExample 1: Basic distribution properties' );
+console.log( 'Parameters: N=%d, K=%d, n=%d', N1, K1, n1 );
+console.log( 'Mean: %d', hypergeometric.mean( N1, K1, n1 ) );
+console.log( 'Variance: %d', hypergeometric.variance( N1, K1, n1 ) );
+console.log( 'Skewness: %d', hypergeometric.skewness( N1, K1, n1 ) );
+console.log( 'Excess Kurtosis: %d', hypergeometric.kurtosis( N1, K1, n1 ) );
+console.log( 'Standard Deviation: %d', hypergeometric.stdev( N1, K1, n1 ) );
+
+// Example 2: PMF and CDF calculations
+var N2 = 100;
+var K2 = 40;
+var n2 = 25;
+
+console.log( '\nExample 2: PMF and CDF calculations' );
+console.log( 'Parameters: N=%d, K=%d, n=%d', N2, K2, n2 );
+for ( var x = 0; x <= 10; x += 2 ) {
+    console.log( 'P(X = %d): %d', x, hypergeometric.pmf( x, N2, K2, n2 ) );
+    console.log( 'P(X <= %d): %d', x, hypergeometric.cdf( x, N2, K2, n2 ) );
+}
+
+// Example 3: Quantile function
+var N3 = 80;
+var K3 = 30;
+var n3 = 20;
+
+console.log( '\nExample 3: Quantile function' );
+console.log( 'Parameters: N=%d, K=%d, n=%d', N3, K3, n3 );
+var probabilities = [ 0.1, 0.25, 0.5, 0.75, 0.9 ];
+for ( var i = 0; i < probabilities.length; i++ ) {
+    var p = probabilities[i];
+    console.log( 'Q(%d): %d', p, hypergeometric.quantile( p, N3, K3, n3 ) );
+}
+
+// Example 4: Random number generation
+var N4 = 60;
+var K4 = 25;
+var n4 = 15;
+
+console.log( '\nExample 4: Random number generation' );
+console.log( 'Parameters: N=%d, K=%d, n=%d', N4, K4, n4 );
+var Hypergeometric = hypergeometric.Hypergeometric;
+var dist = new Hypergeometric( N4, K4, n4 );
+for ( var j = 0; j < 10; j++ ) {
+    console.log( 'Random variate %d: %d', j+1, dist.random() );
+}
+
+// Example 5: Log PMF calculations
+var N5 = 200;
+var K5 = 80;
+var n5 = 50;
+
+console.log( '\nExample 5: Log PMF calculations' );
+console.log( 'Parameters: N=%d, K=%d, n=%d', N5, K5, n5 );
+for ( var y = 10; y <= 30; y += 5 ) {
+    console.log( 'log(P(X = %d)): %d', y, hypergeometric.logpmf( y, N5, K5, n5 ) );
+}
+
+// Example 6: Mode calculation
+var N6 = 75;
+var K6 = 35;
+var n6 = 20;
+
+console.log( '\nExample 6: Mode calculation' );
+console.log( 'Parameters: N=%d, K=%d, n=%d', N6, K6, n6 );
+console.log( 'Mode: %d', hypergeometric.mode( N6, K6, n6 ) );
+
 ```
 
 </section>

lib/node_modules/@stdlib/stats/base/dists/hypergeometric/examples/index.js

@@ -21,4 +21,77 @@
 var objectKeys = require( '@stdlib/utils/keys' );
 var hypergeometric = require( './../lib' );
 
+// Print namespace contents
+console.log( 'Namespace contents:' );
 console.log( objectKeys( hypergeometric ) );
+
+// Example 1: Basic distribution properties
+var N1 = 50; // population size
+var K1 = 20; // number of successes in population
+var n1 = 10; // number of draws
+
+console.log( '\nExample 1: Basic distribution properties' );
+console.log( 'Parameters: N=%d, K=%d, n=%d', N1, K1, n1 );
+console.log( 'Mean: %d', hypergeometric.mean( N1, K1, n1 ) );
+console.log( 'Variance: %d', hypergeometric.variance( N1, K1, n1 ) );
+console.log( 'Skewness: %d', hypergeometric.skewness( N1, K1, n1 ) );
+console.log( 'Excess Kurtosis: %d', hypergeometric.kurtosis( N1, K1, n1 ) );
+console.log( 'Standard Deviation: %d', hypergeometric.stdev( N1, K1, n1 ) );
+
+// Example 2: PMF and CDF calculations
+var N2 = 100;
+var K2 = 40;
+var n2 = 25;
+
+console.log( '\nExample 2: PMF and CDF calculations' );
+console.log( 'Parameters: N=%d, K=%d, n=%d', N2, K2, n2 );
+for ( var x = 0; x <= 10; x += 2 ) {
+	console.log( 'P(X = %d): %d', x, hypergeometric.pmf( x, N2, K2, n2 ) );
+	console.log( 'P(X <= %d): %d', x, hypergeometric.cdf( x, N2, K2, n2 ) );
+}
+
+// Example 3: Quantile function
+var N3 = 80;
+var K3 = 30;
+var n3 = 20;
+
+console.log( '\nExample 3: Quantile function' );
+console.log( 'Parameters: N=%d, K=%d, n=%d', N3, K3, n3 );
+var probabilities = [ 0.1, 0.25, 0.5, 0.75, 0.9 ];
+for ( var i = 0; i < probabilities.length; i++ ) {
+	var p = probabilities[i];
+	console.log( 'Q(%d): %d', p, hypergeometric.quantile( p, N3, K3, n3 ) );
+}
+
+// Example 4: Random number generation
+var N4 = 60;
+var K4 = 25;
+var n4 = 15;
+
+console.log( '\nExample 4: Random number generation' );
+console.log( 'Parameters: N=%d, K=%d, n=%d', N4, K4, n4 );
+var Hypergeometric = hypergeometric.Hypergeometric;
+var dist = new Hypergeometric( N4, K4, n4 );
+for ( var j = 0; j < 10; j++ ) {
+	console.log( 'Random variate %d: %d', j+1, dist.random() );
+}
+
+// Example 5: Log PMF calculations
+var N5 = 200;
+var K5 = 80;
+var n5 = 50;
+
+console.log( '\nExample 5: Log PMF calculations' );
+console.log( 'Parameters: N=%d, K=%d, n=%d', N5, K5, n5 );
+for ( var y = 10; y <= 30; y += 5 ) {
+	console.log( 'log(P(X = %d)): %d', y, hypergeometric.logpmf( y, N5, K5, n5 ) );
+}
+
+// Example 6: Mode calculation
+var N6 = 75;
+var K6 = 35;
+var n6 = 20;
+
+console.log( '\nExample 6: Mode calculation' );
+console.log( 'Parameters: N=%d, K=%d, n=%d', N6, K6, n6 );
+console.log( 'Mode: %d', hypergeometric.mode( N6, K6, n6 ) );