fix: use correct analytic formula and update tests and documentation

---
type: pre_commit_static_analysis_report
description: Results of running static analysis checks when committing changes.
report:
  - task: lint_filenames
    status: passed
  - task: lint_editorconfig
    status: passed
  - task: lint_markdown
    status: passed
  - task: lint_package_json
    status: na
  - task: lint_repl_help
    status: passed
  - task: lint_javascript_src
    status: passed
  - task: lint_javascript_cli
    status: na
  - task: lint_javascript_examples
    status: na
  - task: lint_javascript_tests
    status: passed
  - task: lint_javascript_benchmarks
    status: na
  - task: lint_python
    status: passed
  - task: lint_r
    status: na
  - task: lint_c_src
    status: passed
  - task: lint_c_examples
    status: na
  - task: lint_c_benchmarks
    status: na
  - task: lint_c_tests_fixtures
    status: na
  - task: lint_shell
    status: na
  - task: lint_typescript_declarations
    status: passed
  - task: lint_typescript_tests
    status: passed
  - task: lint_license_headers
    status: passed
---

Author: kgryte

lib/node_modules/@stdlib/stats/base/dists/halfnormal/entropy/README.md

@@ -58,10 +58,10 @@ Returns the [differential entropy][entropy] of a [half-normal][half-normal-distr
 
 ```javascript
 var y = entropy( 1.0 );
-// returns ~1.014
+// returns ~0.7258
 
 y = entropy( 5.0 );
-// returns ~2.624
+// returns ~2.3352
 ```
 
 If provided `sigma ≤ 0`, the function returns `NaN`.
@@ -140,7 +140,7 @@ Returns the differential entropy of a half-normal distribution.
 
 ```c
 double out = stdlib_base_dists_halfnormal_entropy( 1.0 );
-// returns ~1.014
+// returns ~0.7258
 ```
 
 The function accepts the following arguments:

lib/node_modules/@stdlib/stats/base/dists/halfnormal/entropy/docs/repl.txt

@@ -19,9 +19,9 @@
     Examples
     --------
     > var v = {{alias}}( 1.0 )
-    ~1.014
+    ~0.7258
     > v = {{alias}}( 5.0 )
-    ~2.624
+    ~2.3352
 
     See Also
     --------

lib/node_modules/@stdlib/stats/base/dists/halfnormal/entropy/docs/types/index.d.ts

@@ -30,11 +30,11 @@
 *
 * @example
 * var v = entropy( 1.0 );
-* // returns ~1.014
+* // returns ~0.7258
 *
 * @example
 * var v = entropy( 5.0 );
-* // returns ~2.624
+* // returns ~2.3352
 *
 * @example
 * var v = entropy( -0.2 );

lib/node_modules/@stdlib/stats/base/dists/halfnormal/entropy/lib/index.js

@@ -27,10 +27,10 @@
 * var entropy = require( '@stdlib/stats/base/dists/halfnormal/entropy' );
 *
 * var v = entropy( 1.0 );
-* // returns ~1.014
+* // returns ~0.7258
 *
 * v = entropy( 5.0 );
-* // returns ~2.624
+* // returns ~2.3352
 */
 
 // MODULES //

lib/node_modules/@stdlib/stats/base/dists/halfnormal/entropy/lib/main.js

@@ -22,13 +22,12 @@
 
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
 var ln = require( '@stdlib/math/base/special/ln' );
-var GAMMA = require( '@stdlib/constants/float64/eulergamma' );
-var SQRT_HALF_PI = require( '@stdlib/constants/float64/sqrt-half-pi' );
 
 
 // VARIABLES //
 
-var SCALAR = ln( SQRT_HALF_PI ) + ( 0.5*GAMMA ) + 0.5;
+// ( ln(π/2)+1 ) / 2:
+var SCALAR = 0.7257913526447274;
 
 
 // MAIN //
@@ -41,11 +40,11 @@ var SCALAR = ln( SQRT_HALF_PI ) + ( 0.5*GAMMA ) + 0.5;
 *
 * @example
 * var v = entropy( 1.0 );
-* // returns ~1.014
+* // returns ~0.7258
 *
 * @example
 * var v = entropy( 5.0 );
-* // returns ~2.624
+* // returns ~2.3352
 *
 * @example
 * var v = entropy( -0.2 );

lib/node_modules/@stdlib/stats/base/dists/halfnormal/entropy/lib/native.js

@@ -34,11 +34,11 @@ var addon = require( './../src/addon.node' );
 *
 * @example
 * var v = entropy( 1.0 );
-* // returns ~1.014
+* // returns ~0.7258
 *
 * @example
 * var v = entropy( 5.0 );
-* // returns ~2.624
+* // returns ~2.3352
 *
 * @example
 * var v = entropy( -0.2 );

lib/node_modules/@stdlib/stats/base/dists/halfnormal/entropy/manifest.json

@@ -39,7 +39,8 @@
       "libpath": [],
       "dependencies": [
         "@stdlib/math/base/napi/unary",
-        "@stdlib/math/base/assert/is-nan"
+        "@stdlib/math/base/assert/is-nan",
+        "@stdlib/math/base/special/ln"
       ]
     },
     {
@@ -55,6 +56,7 @@
       "libpath": [],
       "dependencies": [
         "@stdlib/math/base/assert/is-nan",
+        "@stdlib/math/base/special/ln",
         "@stdlib/constants/float64/eps"
       ]
     },
@@ -70,7 +72,8 @@
       "libraries": [],
       "libpath": [],
       "dependencies": [
-        "@stdlib/math/base/assert/is-nan"
+        "@stdlib/math/base/assert/is-nan",
+        "@stdlib/math/base/special/ln"
       ]
     }
   ]

lib/node_modules/@stdlib/stats/base/dists/halfnormal/entropy/src/main.c

@@ -17,10 +17,10 @@
 */
 
 #include "stdlib/stats/base/dists/halfnormal/entropy.h"
+#include "stdlib/math/base/special/ln.h"
 #include "stdlib/math/base/assert/is_nan.h"
 
-// 0.5 + ln(sqrt(π/2)) + (eulergamma/2):
-static const double scalar = 1.5143991850954939;
+static const double scalar = 0.7257913526447274; // ( ln(π/2)+1 ) / 2
 
 /**
 * Returns the differential entropy of a half-normal distribution.
@@ -30,11 +30,11 @@ static const double scalar = 1.5143991850954939;
 *
 * @example
 * double y = stdlib_base_dists_halfnormal_entropy( 1.0 );
-* // returns ~1.014
+* // returns ~0.7258
 */
 double stdlib_base_dists_halfnormal_entropy( const double sigma ) {
 	if ( stdlib_base_is_nan( sigma ) || sigma <= 0.0 ) {
 		return 0.0/0.0; // NaN
 	}
-	return stdlib_base_ln( sigma ) + SCALAR;
+	return stdlib_base_ln( sigma ) + scalar;
 }

lib/node_modules/@stdlib/stats/base/dists/halfnormal/entropy/test/fixtures/python/data.json

@@ -20,12 +20,13 @@
 
 import os
 import json
-import numpy as np
 from numpy.random import rand
 from scipy.stats import halfnorm
 
-# Get the file path
+# Get the file path:
 FILE = os.path.realpath(__file__)
+
+# Extract the directory in which this file resides:
 DIR = os.path.dirname(FILE)
 
 
@@ -40,18 +41,16 @@ def gen(x, name):
     # Examples
 
     ``` python
-    python> x = rand(1000) * 10.0 + 1.0
-    python> gen(x, './data.json')
+    python> x = (rand(1000) * 10.0) + 1.0
+    python> gen(x, "data.json")
     ```
     """
-    y = []
-    for s in np.nditer(x):
-        y.append(halfnorm.entropy(scale=float(s)))
+    y = halfnorm.entropy(loc=0.0, scale=x)
 
     # Store data to be written to file as a dictionary:
     data = {
         "sigma": x.tolist(),
-        "expected": y
+        "expected": y.tolist()
     }
 
     # Based on the script directory, create an output filepath: