public void NextNumberSequenceUniform_LeapfrogEstimatedMean_ConvidenceInterval(int sampleSize, double a, double b, RandomNumberSequence.UniformGenerationMode generatorMode)
{
double expectedMean = (a + b) / 2.0;
double expectedStandardDeviation = (b - a) / (2.0 * Math.Sqrt(3.0));
IRandomNumberStream randomStream = GetRandomStream();
Assume.That(randomStream.SplittingApproach.HasFlag(RandomNumberSequence.SplittingApproach.LeapFrog), String.Format("Random Number Generator {0} does not support Leapfrog approach.", randomStream.ToString()));
int numberOfStreams = 5; // use five sub-streams for Pseudo-Random-Number Generators
if (randomStream.Generator is IQuasiRandomNumberGenerator)
{
numberOfStreams = (int)randomStream.Dimension;
}
var sample = new List <double>(sampleSize);
for (int j = 0; j < numberOfStreams; j++)
{
var stream = randomStream.CreateLeapfrogStream(j, numberOfStreams);
int subSampleSize = sampleSize / numberOfStreams;
var subSample = new double[subSampleSize];
stream.NextNumberSequence.Uniform(subSampleSize, subSample, a, b, generatorMode);
sample.AddRange(subSample);
}
/* compute estimated mean and standard deviation: */
double estimatedMean = sample.Average();
double estimatedStandardDeviation = GetEstimatedStandardDeviation(sample.ToArray(), sampleSize, estimatedMean);
double epsilon = 2.0 * estimatedStandardDeviation / Math.Sqrt(sampleSize); // size of the confidence interval w.r.t. normal distribution N{-1}(0.975) \approx 1.96 \approx 2.0, i.e. \alpha/2 quantile with \alpha = 5%
/* test whether E(X) \in [ estimatedMean - \epsilon, estimatedMean + \epsilon], where \epsilon = \sigma/\sqrt(n} */
Assert.That((expectedMean >= estimatedMean - epsilon) && (expectedMean <= estimatedMean + epsilon), String.Format("a: {0}, b: {1}, Expectation: {2}, Standard deviation: {3}, estimated mean: {4}, estimated Standard Deviation: {5}, epsilon: {6}", a, b, expectedMean, expectedStandardDeviation, estimatedMean, estimatedStandardDeviation, epsilon));
}
public void NextNumberSequenceUniform_SkipAheadEstimatedMean_ConvidenceInterval(int sampleSize, double a, double b, RandomNumberSequence.UniformGenerationMode generatorMode)
{
double expectedMean = (a + b) / 2.0;
double expectedStandardDeviation = (b - a) / (2.0 * Math.Sqrt(3.0));
IRandomNumberStream randomStream = GetRandomStream();
Assume.That(randomStream.SplittingApproach.HasFlag(RandomNumberSequence.SplittingApproach.SkipAhead), String.Format("Random Number Generator {0} does not support Leapfrog approach.", randomStream.ToString()));
var sample = new List <double>();
int numberOfStreams = 2;
int nskip = sampleSize * numberOfStreams;
for (int j = 0; j < numberOfStreams; j++)
{
var stream = randomStream.CreateSkipAheadStream(j * nskip);
int subSampleSize = sampleSize / numberOfStreams;
var subSample = new double[subSampleSize];
stream.NextNumberSequence.Uniform(subSampleSize, subSample, a, b, generatorMode);
sample.AddRange(subSample);
}
sampleSize = sample.Count;
/* alternativly, use: */
/*
* var stream1 = randomStream.CreateSkipAheadStream(5);
* var stream2 = stream1.CreateSkipAheadStream(5);
* var stream3 = stream2.CreateSkipAheadStream(5);
*
* int subSampleSize = sampleSize / 3;
* var sample1 = new double[subSampleSize];
* stream1.NextNumberSequence.Uniform(subSampleSize, sample1, a, b, generatorMode);
*
* var sample2 = new double[subSampleSize];
* stream2.NextNumberSequence.Uniform(subSampleSize, sample2, a, b, generatorMode);
*
* var sample3 = new double[subSampleSize];
* stream3.NextNumberSequence.Uniform(subSampleSize, sample3, a, b, generatorMode);
*
* var sample = new List<double>();
* sample.AddRange(sample1);
* sample.AddRange(sample2);
* sample.AddRange(sample3);
*/
/* compute estimated mean and standard deviation: */
double estimatedMean = sample.Average();
double estimatedStandardDeviation = GetEstimatedStandardDeviation(sample.ToArray(), sampleSize, estimatedMean);
double epsilon = 2.0 * estimatedStandardDeviation / Math.Sqrt(sampleSize); // size of the confidence interval w.r.t. normal distribution N{-1}(0.975) \approx 1.96 \approx 2.0, i.e. \alpha/2 quantile with \alpha = 5%
/*
* Even for a fixed seed the results of the random sampling are not identically (for Intel's MKL Library)!
*
* Therefore we enlarge the convidence interval - this unit test is not part of a test suite for Random Number Generators.
* We focus on the integration with the native Dll.
*/
epsilon *= 2.0; // special adjustment, in most cases not necessary
/* test whether E(X) \in [ estimatedMean - \epsilon, estimatedMean + \epsilon], where \epsilon = \sigma/\sqrt(n} */
Assert.That(estimatedMean - epsilon, Is.LessThanOrEqualTo(expectedMean), String.Format("a: {0}, b: {1}, Expectation: {2}, Standard deviation: {3}, estimated mean: {4}, estimated Standard Deviation: {5}, epsilon: {6}", a, b, expectedMean, expectedStandardDeviation, estimatedMean, estimatedStandardDeviation, epsilon));
Assert.That(estimatedMean + epsilon, Is.GreaterThanOrEqualTo(expectedMean), String.Format("a: {0}, b: {1}, Expectation: {2}, Standard deviation: {3}, estimated mean: {4}, estimated Standard Deviation: {5}, epsilon: {6}", a, b, expectedMean, expectedStandardDeviation, estimatedMean, estimatedStandardDeviation, epsilon));
}