fix: return excess kurtosis in stats/base/dists/kumaraswamy/kurtosis

lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/ctor/README.md

@@ -112,7 +112,7 @@ Returns the [excess kurtosis][kurtosis].
 var kumaraswamy = new Kumaraswamy( 4.0, 12.0 );
 
 var kurtosis = kumaraswamy.kurtosis;
-// returns ~2.704
+// returns ~-0.296
 ```
 
 #### Kumaraswamy.prototype.mean

lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/ctor/docs/repl.txt

@@ -56,7 +56,7 @@
     > kumaraswamy.b
     5.0
     > kumaraswamy.kurtosis
-    ~3.194
+    ~0.194
     > kumaraswamy.mean
     ~0.696
     > kumaraswamy.mode

lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/ctor/lib/main.js

@@ -182,7 +182,7 @@ function Kumaraswamy() {
 * var kumaraswamy = new Kumaraswamy( 4.0, 12.0 );
 *
 * var v = kumaraswamy.kurtosis;
-* // returns ~2.704
+* // returns ~-0.296
 */
 setReadOnlyAccessor( Kumaraswamy.prototype, 'kurtosis', function get() {
 	return kurtosis( this.a, this.b );

lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/README.md

@@ -28,13 +28,13 @@ limitations under the License.
 
 The [excess kurtosis][kurtosis] for a [Kumaraswamy's double bounded][kumaraswamy-distribution] random variable with first shape parameter `a` and second shape parameter `b` is
 
-<!-- <equation class="equation" label="eq:kumaraswamy_kurtosis" align="center" raw="\operatorname{Kurt}\left( X \right) = \frac{ m_4 - ( 4.0 \cdot m_3 \cdot m_1 ) + ( 6.0 \cdot m_2 \cdot m_1^2 ) - ( 3.0 \cdot m_1^4 ) ) }{\left( m_2 - m_1^2 \right)^2}" alt="Excess kurtosis for a Kumaraswamy's double bounded distribution."> -->
+<!-- <equation class="equation" label="eq:kumaraswamy_kurtosis" align="center" raw="\operatorname{Kurt}\left( X \right) = \frac{ m_4 - ( 4.0 \cdot m_3 \cdot m_1 ) + ( 6.0 \cdot m_2 \cdot m_1^2 ) - ( 3.0 \cdot m_1^4 ) }{\left( m_2 - m_1^2 \right)^2} - 3" alt="Excess kurtosis for a Kumaraswamy's double bounded distribution."> -->
 
 ```math
-\mathop{\mathrm{Kurt}}\left( X \right) = \frac{ m_4 - ( 4.0 \cdot m_3 \cdot m_1 ) + ( 6.0 \cdot m_2 \cdot m_1^2 ) - ( 3.0 \cdot m_1^4 ) ) }{\left( m_2 - m_1^2 \right)^2}
+\mathop{\mathrm{Kurt}}\left( X \right) = \frac{ m_4 - ( 4.0 \cdot m_3 \cdot m_1 ) + ( 6.0 \cdot m_2 \cdot m_1^2 ) - ( 3.0 \cdot m_1^4 ) }{\left( m_2 - m_1^2 \right)^2} - 3
 ```
 
-<!-- <div class="equation" align="center" data-raw-text="\operatorname{Kurt}\left( X \right) = \frac{ m_4 - ( 4.0 \cdot m_3 \cdot m_1 ) + ( 6.0 \cdot m_2 \cdot m_1^2 ) - ( 3.0 \cdot m_1^4 ) ) }{\left( m_2 - m_1^2 \right)^2}" data-equation="eq:kumaraswamy_kurtosis">
+<!-- <div class="equation" align="center" data-raw-text="\operatorname{Kurt}\left( X \right) = \frac{ m_4 - ( 4.0 \cdot m_3 \cdot m_1 ) + ( 6.0 \cdot m_2 \cdot m_1^2 ) - ( 3.0 \cdot m_1^4 ) }{\left( m_2 - m_1^2 \right)^2} - 3" data-equation="eq:kumaraswamy_kurtosis">
     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/docs/img/equation_kumaraswamy_kurtosis.svg" alt="Excess kurtosis for a Kumaraswamy's double bounded distribution.">
     <br>
 </div> -->
@@ -78,13 +78,13 @@ Returns the [excess kurtosis][kurtosis] of a [Kumaraswamy's double bounded][kuma
 
 ```javascript
 var v = kurtosis( 1.0, 1.0 );
-// returns ~1.8
+// returns ~-1.2
 
 v = kurtosis( 4.0, 12.0 );
-// returns ~2.704
+// returns ~-0.296
 
 v = kurtosis( 2.0, 8.0 );
-// returns ~2.666
+// returns ~-0.334
 ```
 
 If provided `NaN` as any argument, the function returns `NaN`.
@@ -187,7 +187,7 @@ Returns the [excess kurtosis][kurtosis] of a [Kumaraswamy's double bounded][kuma
 
 ```c
 double v = stdlib_base_dists_kumaraswamy_kurtosis( 0.5, 1.0 );
-// returns ~2.143
+// returns ~-0.857
 ```
 
 The function accepts the following arguments:

lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/docs/repl.txt

@@ -22,11 +22,11 @@
     Examples
     --------
     > var v = {{alias}}( 1.0, 1.0 )
-    ~1.8
+    ~-1.2
     > v = {{alias}}( 4.0, 12.0 )
-    ~2.704
+    ~-0.296
     > v = {{alias}}( 16.0, 8.0 )
-    ~4.311
+    ~1.311
 
     See Also
     --------

lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/docs/types/index.d.ts

@@ -31,15 +31,15 @@
 *
 * @example
 * var v = kurtosis( 0.5, 1.0 );
-* // returns ~2.143
+* // returns ~-0.857
 *
 * @example
 * var v = kurtosis( 4.0, 12.0 );
-* // returns ~2.704
+* // returns ~-0.296
 *
 * @example
 * var v = kurtosis( 12.0, 2.0 );
-* // returns ~4.817
+* // returns ~1.817
 *
 * @example
 * var v = kurtosis( 1.0, -0.1 );

lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/lib/index.js

@@ -27,13 +27,13 @@
 * var kurtosis = require( '@stdlib/stats/base/dists/kumaraswamy/kurtosis' );
 *
 * var v = kurtosis( 2.0, 1.0 );
-* // returns ~2.4
+* // returns ~-0.6
 *
 * v = kurtosis( 4.0, 12.0 );
-* // returns ~2.704
+* // returns ~-0.296
 *
 * v = kurtosis( 16.0, 8.0 );
-* // returns ~4.311
+* // returns ~1.311
 */
 
 // MODULES //

lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/lib/main.js

@@ -35,15 +35,15 @@ var beta = require( '@stdlib/math/base/special/beta' );
 *
 * @example
 * var v = kurtosis( 0.5, 1.0 );
-* // returns ~2.143
+* // returns ~-0.857
 *
 * @example
 * var v = kurtosis( 4.0, 12.0 );
-* // returns ~2.704
+* // returns ~-0.296
 *
 * @example
 * var v = kurtosis( 12.0, 2.0 );
-* // returns ~4.817
+* // returns ~1.817
 *
 * @example
 * var v = kurtosis( 1.0, -0.1 );
@@ -85,7 +85,7 @@ function kurtosis( a, b ) {
 	mu2 = m1 * m1;
 	out = ( m4 - ( 4.0*m3*m1 ) + ( 6.0*m2*mu2 ) - ( 3.0*mu2*mu2 ) );
 	out /= sigma2*sigma2;
-	return out;
+	return out - 3.0;
 }
 
 

lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/lib/native.js

@@ -35,15 +35,15 @@ var addon = require( './../src/addon.node' );
 *
 * @example
 * var v = kurtosis( 0.5, 1.0 );
-* // returns ~2.143
+* // returns ~-0.857
 *
 * @example
 * var v = kurtosis( 4.0, 12.0 );
-* // returns ~2.704
+* // returns ~-0.296
 *
 * @example
 * var v = kurtosis( 12.0, 2.0 );
-* // returns ~4.817
+* // returns ~1.817
 *
 * @example
 * var v = kurtosis( 1.0, -0.1 );

lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/src/main.c

@@ -29,7 +29,7 @@
 *
 * @example
 * double v = stdlib_base_dists_kumaraswamy_kurtosis( 0.5, 1.0 );
-* // returns ~2.143
+* // returns ~-0.857
 */
 double stdlib_base_dists_kumaraswamy_kurtosis( const double a, const double b ) {
 	double sigma2;
@@ -55,6 +55,6 @@ double stdlib_base_dists_kumaraswamy_kurtosis( const double a, const double b )
 	mu2 = m1 * m1;
 	out = ( m4 - ( 4.0*m3*m1 ) + ( 6.0*m2*mu2 ) - ( 3.0*mu2*mu2 ) );
 	out /= sigma2*sigma2;
-	return out;
+	return out - 3.0;
 }
 

lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/test/fixtures/julia/REQUIRE

@@ -0,0 +1,3 @@
+Distributions 0.23.8
+julia 1.5
+JSON 0.21

lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/test/fixtures/julia/runner.jl

@@ -0,0 +1,73 @@
+#!/usr/bin/env julia
+#
+# @license Apache-2.0
+#
+# Copyright (c) 2026 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: kurtosis, Kumaraswamy
+import JSON
+
+"""
+	gen( a, b, name )
+
+Generate fixture data and write to file.
+
+# Arguments
+
+* `a`: shape parameter a (must be positive)
+* `b`: shape parameter b (must be positive)
+* `name::AbstractString`: output filename
+
+# Examples
+
+``` julia
+julia> a = rand( 1000 );
+julia> b = rand( 1000 );
+julia> gen( a, b, \"data.json\" );
+```
+"""
+function gen( a, b, name )
+	z = Array{Float64}( undef, length(a) );
+	for i in eachindex(a)
+		z[ i ] = kurtosis( Kumaraswamy( a[ i ], b[ i ] ) );
+	end
+
+	# Store data to be written to file as a collection:
+	data = Dict([
+		("a", a),
+		("b", b),
+		("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) );
+	write( outfile, "\n" );
+	close( outfile );
+end
+
+# Get the filename:
+file = @__FILE__;
+
+# Extract the directory in which this file resides:
+dir = dirname( file );
+
+# Generate fixtures:
+a = rand( 1000 );
+b = rand( 1000 );
+gen( a, b, "data.json" );

lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/test/test.js

@@ -21,15 +21,18 @@
 // MODULES //
 
 var tape = require( 'tape' );
-var isNumber = require( '@stdlib/assert/is-number' ).isPrimitive;
+var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
-var randu = require( '@stdlib/random/base/randu' );
 var PINF = require( '@stdlib/constants/float64/pinf' );
 var NINF = require( '@stdlib/constants/float64/ninf' );
-var EPS = require( '@stdlib/constants/float64/eps' );
 var kurtosis = require( './../lib' );
 
 
+// FIXTURES //
+
+var data = require( './fixtures/julia/data.json' );
+
+
 // TESTS //
 
 tape( 'main export is a function', function test( t ) {
@@ -100,17 +103,18 @@ tape( 'if provided a nonpositive `b`, the function returns `NaN`', function test
 });
 
 tape( 'the function returns the excess kurtosis of a Kumaraswamy\'s double bounded distribution', function test( t ) {
+	var expected;
 	var a;
 	var b;
 	var i;
 	var y;
 
-	// TODO: Add fixtures
-	for ( i = 0; i < 100; i++ ) {
-		a = ( randu()*5.0 ) + EPS;
-		b = ( randu()*5.0 ) + EPS;
-		y = kurtosis( a, b );
-		t.strictEqual( isNumber( y ), true, 'returns expected value' );
+	expected = data.expected;
+	a = data.a;
+	b = data.b;
+	for ( i = 0; i < expected.length; i++ ) {
+		y = kurtosis( a[i], b[i] );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 1043762 ), true, 'returns expected value' );
 	}
 	t.end();
 });

lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/test/test.native.js

@@ -23,12 +23,15 @@
 var resolve = require( 'path' ).resolve;
 var tape = require( 'tape' );
 var tryRequire = require( '@stdlib/utils/try-require' );
-var isNumber = require( '@stdlib/assert/is-number' ).isPrimitive;
+var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
-var randu = require( '@stdlib/random/base/randu' );
 var PINF = require( '@stdlib/constants/float64/pinf' );
 var NINF = require( '@stdlib/constants/float64/ninf' );
-var EPS = require( '@stdlib/constants/float64/eps' );
+
+
+// FIXTURES //
+
+var data = require( './fixtures/julia/data.json' );
 
 
 // VARIABLES //
@@ -112,17 +115,18 @@ tape( 'if provided a nonpositive `b`, the function returns `NaN`', opts, functio
 });
 
 tape( 'the function returns the excess kurtosis of a Kumaraswamy\'s double bounded distribution', opts, function test( t ) {
+	var expected;
 	var a;
 	var b;
 	var i;
 	var y;
 
-	// TODO: Add fixtures
-	for ( i = 0; i < 100; i++ ) {
-		a = ( randu()*5.0 ) + EPS;
-		b = ( randu()*5.0 ) + EPS;
-		y = kurtosis( a, b );
-		t.strictEqual( isNumber( y ), true, 'returns expected value' );
+	expected = data.expected;
+	a = data.a;
+	b = data.b;
+	for ( i = 0; i < expected.length; i++ ) {
+		y = kurtosis( a[i], b[i] );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 1043762 ), true, 'returns expected value' );
 	}
 	t.end();
 });