public void ShapiroWilkTest()
{
// Tested against R's shapiro.test(x)
double[] samples =
{
0.11, 7.87, 4.61, 10.14, 7.95, 3.14, 0.46, 4.43,
0.21, 4.75, 0.71, 1.52, 3.24, 0.93, 0.42, 4.97,
9.53, 4.55, 0.47, 6.66
};
/*
samples <- c(0.11, 7.87, 4.61, 10.14, 7.95, 3.14, 0.46, 4.43, 0.21,
+ 4.75, 0.71, 1.52, 3.24, 0.93, 0.42, 4.97, 9.53, 4.55, 0.47, 6.66)
shapiro.test(samples)
W = 0.90050, p-value = 0.04209
*/
var target = new ShapiroWilkTest(samples);
Assert.AreEqual(0.90050, target.Statistic, 1e-4);
Assert.AreEqual(0.04209, target.PValue, 1e-5);
}
public void ShapiroWilkTest()
{
// Tested against R's shapiro.test(x)
double[] samples =
{
0.11, 7.87, 4.61, 10.14, 7.95, 3.14, 0.46, 4.43,
0.21, 4.75, 0.71, 1.52, 3.24, 0.93, 0.42, 4.97,
9.53, 4.55, 0.47, 6.66
};
/*
* samples <- c(0.11, 7.87, 4.61, 10.14, 7.95, 3.14, 0.46, 4.43, 0.21,
+ 4.75, 0.71, 1.52, 3.24, 0.93, 0.42, 4.97, 9.53, 4.55, 0.47, 6.66)
+
+ shapiro.test(samples)
+
+ W = 0.90050, p-value = 0.04209
*/
var target = new ShapiroWilkTest(samples);
Assert.AreEqual(0.90050, target.Statistic, 1e-4);
Assert.AreEqual(0.04209, target.PValue, 1e-5);
}
public void RNGVentura_ShapiroWilkTest_Has_Significant_Deviation_From_Normal_Distribution()
{
double[] sample = GenerateFloatingPointNumberArray();
var swTest = new ShapiroWilkTest(sample);
// significant deviation from a normal distribution
swTest.Significant.Should().BeTrue();
}
protected override void EndProcessing()
{
var test = new ShapiroWilkTest(_data.ToArray())
{
Size = Size
};
WriteObject(test);
}
public void ShapiroWilkTest()
{
// Tested against R's shapiro.test(x)
#region doc_test
// Let's say we would like to determine whether a set
// of observations come from a normal distribution:
double[] samples =
{
0.11, 7.87, 4.61, 10.14, 7.95, 3.14, 0.46, 4.43,
0.21, 4.75, 0.71, 1.52, 3.24, 0.93, 0.42, 4.97,
9.53, 4.55, 0.47, 6.66
};
// For this, we can use the Shapiro-Wilk test. This test tests the null hypothesis
// that samples come from a Normal distribution, vs. the alternative hypothesis that
// the samples do not come from such distribution. In other words, should this test
// come out significant, it means our samples do not come from a Normal distribution.
// Create a new Shapiro-Wilk test:
var sw = new ShapiroWilkTest(samples);
double W = sw.Statistic; // should be 0.90050
double p = sw.PValue; // should be 0.04209
bool significant = sw.Significant; // should be true
// The test is significant, therefore we should reject the null
// hypothesis that the samples come from a Normal distribution.
#endregion
/*
* samples <- c(0.11, 7.87, 4.61, 10.14, 7.95, 3.14, 0.46, 4.43, 0.21,
+ 4.75, 0.71, 1.52, 3.24, 0.93, 0.42, 4.97, 9.53, 4.55, 0.47, 6.66)
+
+ shapiro.test(samples)
+
+ W = 0.90050, p-value = 0.04209
*/
Assert.AreEqual(0.90050, W, 1e-4);
Assert.AreEqual(0.04209, p, 1e-5);
Assert.IsTrue(significant);
}
public void ShapiroWilkTest2()
{
// Tested against R's shapiro.test(x)
double[] samples =
{
1.36, 1.14, 2.92, 2.55, 1.46, 1.06, 5.27, 1.11, 3.48,
1.10, 0.88, 0.51, 1.46, 0.52, 6.20, 1.69, 0.08, 3.67,
2.81, 3.49
};
/*
* samples <- c(1.36, 1.14, 2.92, 2.55, 1.46, 1.06, 5.27, 1.11, 3.48, +
* 1.10, 0.88, 0.51, 1.46, 0.52, 6.20, 1.69, 0.08, 3.67, 2.81, 3.49)
*
* W = 0.89090000, p-value = 0.02798
*/
var target = new ShapiroWilkTest(samples);
Assert.AreEqual(0.89090, target.Statistic, 1e-4);
Assert.AreEqual(0.02798, target.PValue, 1e-5);
}
public void ShapiroWilkTest2()
{
// Tested against R's shapiro.test(x)
double[] samples =
{
1.36, 1.14, 2.92, 2.55, 1.46, 1.06, 5.27, 1.11, 3.48,
1.10, 0.88, 0.51, 1.46, 0.52, 6.20, 1.69, 0.08, 3.67,
2.81, 3.49
};
/*
samples <- c(1.36, 1.14, 2.92, 2.55, 1.46, 1.06, 5.27, 1.11, 3.48, +
1.10, 0.88, 0.51, 1.46, 0.52, 6.20, 1.69, 0.08, 3.67, 2.81, 3.49)
W = 0.89090000, p-value = 0.02798
*/
var target = new ShapiroWilkTest(samples);
Assert.AreEqual(0.89090, target.Statistic, 1e-4);
Assert.AreEqual(0.02798, target.PValue, 1e-5);
}
public void UniformDistributionTest(double[] sampleArr, double lowerBound, double upperBound)
{
Array.Sort(sampleArr);
RunningStatistics runningStats = new RunningStatistics(sampleArr);
// Skewness should be pretty close to zero (evenly distributed samples)
if (Math.Abs(runningStats.Skewness) > 0.01) Assert.Fail();
// Mean test.
double range = upperBound - lowerBound;
double expectedMean = lowerBound + (range / 2.0);
double meanErr = expectedMean - runningStats.Mean;
double maxExpectedErr = range / 1000.0;
if (Math.Abs(meanErr) > maxExpectedErr) Assert.Fail();
for (double tau = 0; tau <= 1.0; tau += 0.01)
{
double quantile = SortedArrayStatistics.Quantile(sampleArr, tau);
double expectedQuantile = lowerBound + (tau * range);
double quantileError = expectedQuantile - quantile;
if (Math.Abs(quantileError) > maxExpectedErr) Assert.Fail();
}
ShapiroWilkTest test = new ShapiroWilkTest(sampleArr);
Assert.True(test.Significant);
}
public void TestBoxMullerTransformationClamped()
{
BoxMullerTransformation boxMullerTransformation = new BoxMullerTransformation(RandomGenerator.GetInstance());
double[] values = Enumerable.Range(0, 1000000).Select(i => boxMullerTransformation.NextBoundedGaussian(3,2,10)).ToArray();
ShapiroWilkTest test = new ShapiroWilkTest(values);
Assert.True(test.Significant);
}
