diff --git a/FastRngTests/Double/Distributions/CauchyLorentz.cs b/FastRngTests/Double/Distributions/CauchyLorentzX0.cs
similarity index 56%
rename from FastRngTests/Double/Distributions/CauchyLorentz.cs
rename to FastRngTests/Double/Distributions/CauchyLorentzX0.cs
index c2b1cfa..97a61a3 100644
--- a/FastRngTests/Double/Distributions/CauchyLorentz.cs
+++ b/FastRngTests/Double/Distributions/CauchyLorentzX0.cs
@@ -8,12 +8,43 @@ using NUnit.Framework;
 namespace FastRngTests.Double.Distributions
 {
     [ExcludeFromCodeCoverage]
-    public class CauchyLorentz
+    public class CauchyLorentzX0
     {
-        public void TestCauchyDistribution01()
+        [Test]
+        [Category(TestCategories.COVER)]
+        [Category(TestCategories.NORMAL)]
+        public async Task TestCauchyDistribution01()
         {
             // The properties of the cauchy distribution cannot be tested by mean, media or variance,  
             // cf. https://en.wikipedia.org/wiki/Cauchy_distribution#Explanation_of_undefined_moments
+            
+            var dist = new FastRng.Double.Distributions.CauchyLorentzX0();
+            var fqa = new FrequencyAnalysis();
+            var rng = new MultiThreadedRng();
+            
+            for (var n = 0; n < 100_000; n++)
+                fqa.CountThis(await rng.NextNumber(dist));
+            
+            rng.StopProducer();
+            var result = fqa.NormalizeAndPlotEvents(TestContext.WriteLine);
+            
+            Assert.That(result[0], Is.EqualTo(0.976990739772031).Within(0.04));
+            Assert.That(result[1], Is.EqualTo(0.948808314586299).Within(0.06));
+            Assert.That(result[2], Is.EqualTo(0.905284997403441).Within(0.05));
+            
+            Assert.That(result[21], Is.EqualTo(0.168965864241396).Within(0.04));
+            Assert.That(result[22], Is.EqualTo(0.156877686354491).Within(0.04));
+            Assert.That(result[23], Is.EqualTo(0.145970509936354).Within(0.04));
+            
+            Assert.That(result[50], Is.EqualTo(0.036533159835978).Within(0.01));
+            
+            Assert.That(result[75], Is.EqualTo(0.016793067514802).Within(0.01));
+            Assert.That(result[85], Is.EqualTo(0.01316382933791).Within(0.005));
+            Assert.That(result[90], Is.EqualTo(0.011773781734516).Within(0.005));
+            
+            Assert.That(result[97], Is.EqualTo(0.010168596941156).Within(0.005));
+            Assert.That(result[98], Is.EqualTo(0.009966272570142).Within(0.005));
+            Assert.That(result[99], Is.EqualTo(0.00976990739772).Within(0.005));
         }
 
         [Test]
@@ -21,10 +52,11 @@ namespace FastRngTests.Double.Distributions
         [Category(TestCategories.NORMAL)]
         public async Task TestCauchyGeneratorWithRange01()
         {
+            var dist = new FastRng.Double.Distributions.CauchyLorentzX0();
             var rng = new MultiThreadedRng();
             var samples = new double[1_000];
             for (var n = 0; n < samples.Length; n++)
-                samples[n] = await rng.NextNumber(-1.0, 1.0, new FastRng.Double.Distributions.CauchyLorentz());
+                samples[n] = await rng.NextNumber(-1.0, 1.0, dist);
             
             rng.StopProducer();
             Assert.That(samples.Min(), Is.GreaterThanOrEqualTo(-1.0), "Min is out of range");
@@ -36,10 +68,11 @@ namespace FastRngTests.Double.Distributions
         [Category(TestCategories.NORMAL)]
         public async Task TestCauchyGeneratorWithRange02()
         {
+            var dist = new FastRng.Double.Distributions.CauchyLorentzX0();
             var rng = new MultiThreadedRng();
             var samples = new double[1_000];
             for (var n = 0; n < samples.Length; n++)
-                samples[n] = await rng.NextNumber(0.0, 1.0, new FastRng.Double.Distributions.CauchyLorentz());
+                samples[n] = await rng.NextNumber(0.0, 1.0, dist);
             
             rng.StopProducer();
             Assert.That(samples.Min(), Is.GreaterThanOrEqualTo(0.0), "Min is out of range");
@@ -52,7 +85,7 @@ namespace FastRngTests.Double.Distributions
         public async Task TestCauchyGeneratorWithRange03()
         {
             var rng = new MultiThreadedRng();
-            var dist = new FastRng.Double.Distributions.CauchyLorentz { Random = rng }; // Test default parameters
+            var dist = new FastRng.Double.Distributions.CauchyLorentzX0 { Random = rng }; // Test default parameters
             
             var samples = new double[1_000];
             for (var n = 0; n < samples.Length; n++)
@@ -68,7 +101,7 @@ namespace FastRngTests.Double.Distributions
         [Category(TestCategories.NORMAL)]
         public async Task NoRandomNumberGenerator01()
         {
-            var dist = new FastRng.Double.Distributions.CauchyLorentz();
+            var dist = new FastRng.Double.Distributions.CauchyLorentzX0();
             Assert.DoesNotThrowAsync(async () => await dist.GetDistributedValue());
             Assert.That(await dist.GetDistributedValue(), Is.NaN);
         }