public void TheoreticalDistributionTest_with_reestimation()
{
Accord.Math.Random.Generator.Seed = 1;
double[] sample = { 1, 5, 3, 1, 5, 2, 1 };
UnivariateContinuousDistribution distribution = NormalDistribution.Standard;
var target = new LillieforsTest(sample, distribution);
ISampleableDistribution <double> actual = target.TheoreticalDistribution;
Assert.AreEqual(distribution, actual);
}
public void RNGVentura_LillieforsTest_Has_Significant_Deviation_From_Normal_Distribution()
{
double[] sample = GenerateFloatingPointNumberArray();
var distribution = UniformContinuousDistribution.Estimate(sample);
var ndistribution = NormalDistribution.Estimate(sample);
var lillie = new LillieforsTest(sample, distribution);
var nlillie = new LillieforsTest(sample, ndistribution);
// no significant deviation from a uniform continuous distribution estimate
lillie.Significant.Should().BeFalse();
// significant deviation from a normal distribution
nlillie.Significant.Should().BeTrue();
}
public void KolmogorovSmirnovTestConstructorTest()
{
#region doc_uniform_ks
// Test against a standard Uniform distribution
// References: http://www.math.nsysu.edu.tw/~lomn/homepage/class/92/kstest/kolmogorov.pdf
// Make this example reproducible
Accord.Math.Random.Generator.Seed = 1;
// Suppose we got a new sample, and we would like to test whether this
// sample seems to have originated from a uniform continuous distribution.
//
double[] sample =
{
0.621, 0.503, 0.203, 0.477, 0.710, 0.581, 0.329, 0.480, 0.554, 0.382
};
// First, we create the distribution we would like to test against:
//
var distribution = UniformContinuousDistribution.Standard;
// Now we can define our hypothesis. The null hypothesis is that the sample
// comes from a standard uniform distribution, while the alternate is that
// the sample is not from a standard uniform distribution.
//
var kstest = new LillieforsTest(sample, distribution, reestimate: false, iterations: 10 * 1000 * 1000);
double statistic = kstest.Statistic; // 0.29
double pvalue = kstest.PValue; // 0.3067
bool significant = kstest.Significant; // false
// Since the null hypothesis could not be rejected, then the sample
// can perhaps be from a uniform distribution. However, please note
// that this doesn't means that the sample *is* from the uniform, it
// only means that we could not rule out the possibility.
#endregion
Assert.AreEqual(distribution, kstest.TheoreticalDistribution);
Assert.AreEqual(KolmogorovSmirnovTestHypothesis.SampleIsDifferent, kstest.Hypothesis);
Assert.AreEqual(DistributionTail.TwoTail, kstest.Tail);
Assert.AreEqual(0.29, statistic, 1e-16);
Assert.AreEqual(0.3067, pvalue, 2e-3);
Assert.IsFalse(Double.IsNaN(pvalue));
Assert.IsFalse(kstest.Significant);
}
public void KolmogorovSmirnovTestConstructorTest2()
{
#region doc_normal_ks
// Test against a Normal distribution
// Make this example reproducible
Accord.Math.Random.Generator.Seed = 1;
// This time, let's see if the same sample from the previous example
// could have originated from a standard Normal (Gaussian) distribution.
//
double[] sample =
{
0.621, 0.503, 0.203, 0.477, 0.710, 0.581, 0.329, 0.480, 0.554, 0.382
};
// Before we could not rule out the possibility that the sample came from
// a uniform distribution, which means the sample was not very far from
// uniform. This would be an indicative that it would be far from what
// would be expected from a Normal distribution:
NormalDistribution distribution = NormalDistribution.Standard;
var kstest = new LillieforsTest(sample, distribution, reestimate: false);
double statistic = kstest.Statistic; // 0.580432
double pvalue = kstest.PValue; // 0.000999
bool significant = kstest.Significant; // true
// Since the test says that the null hypothesis should be rejected, then
// this can be regarded as a strong indicative that the sample does not
// comes from a Normal distribution, just as we expected.
#endregion
Assert.AreEqual(distribution, kstest.TheoreticalDistribution);
Assert.AreEqual(KolmogorovSmirnovTestHypothesis.SampleIsDifferent, kstest.Hypothesis);
Assert.AreEqual(DistributionTail.TwoTail, kstest.Tail);
Assert.AreEqual(0.580432, kstest.Statistic, 1e-5);
Assert.AreEqual(0.000999, kstest.PValue, 1e-3);
Assert.IsFalse(Double.IsNaN(kstest.Statistic));
// The null hypothesis can be rejected:
// the sample is not from a standard Normal distribution
Assert.IsTrue(kstest.Significant);
}
public void KolmogorovSmirnovTestConstructorTest2_with_reestimation()
{
#region doc_normal
// Test against a Normal distribution
// Make this example reproducible
Accord.Math.Random.Generator.Seed = 1;
// This time, let's see if the same sample from the previous example
// could have originated from a fitted Normal (Gaussian) distribution.
//
double[] sample =
{
0.021, 0.003, 0.203, 0.177, 0.910, 0.881, 0.929, 0.180, 0.854, 0.982
};
// Before we could not rule out the possibility that the sample came from
// a uniform distribution, which means the sample was not very far from
// uniform. This would be an indicative that it would be far from what
// would be expected from a Normal distribution:
NormalDistribution distribution = NormalDistribution.Estimate(sample);
// Create the test
var lillie = new LillieforsTest(sample, distribution);
double statistic = lillie.Statistic; // 0.2882
double pvalue = lillie.PValue; // 0.0207
bool significant = lillie.Significant; // true
// Since the test says that the null hypothesis should be rejected, then
// this can be regarded as a strong indicative that the sample does not
// comes from a Normal distribution, just as we expected.
#endregion
Assert.AreEqual(distribution, lillie.TheoreticalDistribution);
Assert.AreEqual(KolmogorovSmirnovTestHypothesis.SampleIsDifferent, lillie.Hypothesis);
Assert.AreEqual(DistributionTail.TwoTail, lillie.Tail);
Assert.AreEqual(0.28823410018244089, lillie.Statistic, 1e-5);
Assert.IsTrue(lillie.PValue < 0.03);
// The null hypothesis can be rejected:
// the sample is not from a standard Normal distribution
Assert.IsTrue(lillie.Significant);
}
public void KolmogorovSmirnovTestConstructorTest_with_reestimation()
{
#region doc_uniform
// Test against a Uniform distribution fitted from the data
// Make this example reproducible
Accord.Math.Random.Generator.Seed = 1;
// Suppose we got a new sample, and we would like to test whether this
// sample seems to have originated from a uniform continuous distribution.
//
double[] sample =
{
0.021, 0.003, 0.203, 0.177, 0.910, 0.881, 0.929, 0.180, 0.854, 0.982
};
// First, we create the distribution we would like to test against:
//
var distribution = UniformContinuousDistribution.Estimate(sample);
// Now we can define our hypothesis. The null hypothesis is that the sample
// comes from a standard uniform distribution, while the alternate is that
// the sample is not from a standard uniform distribution.
//
var lillie = new LillieforsTest(sample, distribution, iterations: 10 * 1000 * 1000);
double statistic = lillie.Statistic; // 0.36925
double pvalue = lillie.PValue; // 0.09057
bool significant = lillie.Significant; // false
// Since the null hypothesis could not be rejected, then the sample
// can perhaps be from a uniform distribution. However, please note
// that this doesn't means that the sample *is* from the uniform, it
// only means that we could not rule out the possibility.
#endregion
Assert.AreEqual(distribution, lillie.TheoreticalDistribution);
Assert.AreEqual(KolmogorovSmirnovTestHypothesis.SampleIsDifferent, lillie.Hypothesis);
Assert.AreEqual(DistributionTail.TwoTail, lillie.Tail);
Assert.AreEqual(0.36925434116445355, statistic, 1e-16);
Assert.AreEqual(0.090571500000000027, pvalue, 5e-3);
Assert.IsFalse(lillie.Significant);
}
public void EmpiricalDistributionTest_with_reestimation()
{
Accord.Math.Random.Generator.Seed = 1;
double[] sample = { 1, 5, 3, 1, 5, 2, 1 };
UnivariateContinuousDistribution distribution = NormalDistribution.Standard;
var target = new LillieforsTest(sample, distribution);
EmpiricalDistribution actual = target.EmpiricalDistribution;
Assert.AreNotSame(sample, actual.Samples);
Array.Sort(sample);
for (int i = 0; i < sample.Length; i++)
{
Assert.AreEqual(sample[i], actual.Samples[i]);
}
}
public void KolmogorovSmirnovTestConstructorTest4_with_reestimation()
{
Accord.Math.Random.Generator.Seed = 1;
// Test if the sample's distribution is smaller than a standard Normal distribution
double[] sample = { 0.621, 0.503, 0.203, 0.477, 0.710, 0.581, 0.329, 0.480, 0.554, 0.382 };
NormalDistribution distribution = NormalDistribution.Standard;
var target = new LillieforsTest(sample, distribution,
KolmogorovSmirnovTestHypothesis.SampleIsSmaller);
Assert.AreEqual(distribution, target.TheoreticalDistribution);
Assert.AreEqual(KolmogorovSmirnovTestHypothesis.SampleIsSmaller, target.Hypothesis);
Assert.AreEqual(DistributionTail.OneLower, target.Tail);
Assert.AreEqual(0.580432, target.Statistic, 1e-5);
Assert.AreEqual(0.000499, target.PValue, 5e-4);
Assert.IsFalse(Double.IsNaN(target.Statistic));
}
public void KolmogorovSmirnovTestConstructorTest3()
{
Accord.Math.Random.Generator.Seed = 1;
// Test if the sample's distribution is greater than a standard Normal distribution.
double[] sample = { 0.621, 0.503, 0.203, 0.477, 0.710, 0.581, 0.329, 0.480, 0.554, 0.382 };
NormalDistribution distribution = NormalDistribution.Standard;
var target = new LillieforsTest(sample, distribution, reestimate: false,
alternate: KolmogorovSmirnovTestHypothesis.SampleIsGreater, iterations: 1000 * 1000);
Assert.AreEqual(distribution, target.TheoreticalDistribution);
Assert.AreEqual(KolmogorovSmirnovTestHypothesis.SampleIsGreater, target.Hypothesis);
Assert.AreEqual(DistributionTail.OneUpper, target.Tail);
Assert.AreEqual(0.238852, target.Statistic, 1e-5);
Assert.AreEqual(0.275544, target.PValue, 5e-3);
Assert.IsFalse(Double.IsNaN(target.Statistic));
}
