public static void Main()
{
for (int i = 0; i < 10; i++)
{
Console.WriteLine(SimpleRNG.GetUint());
}
}
static void KSTest()
{
/// Kolmogorov-Smirnov test for distributions. See Knuth volume 2, page 48-51 (third edition).
/// This test should *fail* on average one time in 1000 runs.
/// That's life with random number generators: if the test passed all the time,
/// the source wouldn't be random enough! If the test were to fail more frequently,
/// the most likely explanation would be a bug in the code.
SimpleRNG.SetSeedFromSystemTime();
int numReps = 1000;
double failureProbability = 0.001; // probability of test failing with normal input
int j;
double[] samples = new double[numReps];
for (j = 0; j != numReps; ++j)
{
samples[j] = SimpleRNG.GetUniform();
}
System.Array.Sort(samples);
double CDF;
double temp;
int j_minus = 0, j_plus = 0;
double K_plus = -double.MaxValue;
double K_minus = -double.MaxValue;
for (j = 0; j != numReps; ++j)
{
CDF = samples[j];
temp = (j + 1.0) / numReps - CDF;
if (K_plus < temp)
{
K_plus = temp;
j_plus = j;
}
temp = CDF - (j + 0.0) / numReps;
if (K_minus < temp)
{
K_minus = temp;
j_minus = j;
}
}
double sqrtNumReps = Math.Sqrt((double)numReps);
K_plus *= sqrtNumReps;
K_minus *= sqrtNumReps;
// We divide the failure probability by four because we have four tests:
// left and right tests for K+ and K-.
double p_low = 0.25 * failureProbability;
double p_high = 1.0 - 0.25 * failureProbability;
double cutoff_low = Math.Sqrt(0.5 * Math.Log(1.0 / (1.0 - p_low))) - 1.0 / (6.0 * sqrtNumReps);
double cutoff_high = Math.Sqrt(0.5 * Math.Log(1.0 / (1.0 - p_high))) - 1.0 / (6.0 * sqrtNumReps);
Console.WriteLine("\n\nTesting the random number distribution");
Console.WriteLine("using the Kolmogorov-Smirnov (KS) test.\n");
Console.WriteLine("K+ statistic: {0}", K_plus);
Console.WriteLine("K+ statistic: {0}", K_minus);
Console.WriteLine("Acceptable interval: [{0}, {1}]", cutoff_low, cutoff_high);
Console.WriteLine("K+ max at {0} {1}", j_plus, samples[j_plus]);
Console.WriteLine("K- max at {0} {1}", j_minus, samples[j_minus]);
if (cutoff_low <= K_plus && K_plus <= cutoff_high && cutoff_low <= K_minus && K_minus <= cutoff_high)
{
Console.WriteLine("\nKS test passed\n");
}
else
{
Console.WriteLine("\nKS test failed\n");
}
}
// Verify that distributions have the correct mean and variance.
// Note that sample mean and sample variance will not exactly match the expected mean and variance.
static void TestDistributions()
{
const int numSamples = 100000;
double mean, variance, stdev, shape, scale, degreesOfFreedom;
RunningStat rs = new RunningStat();
// Exponential distribution
rs.Clear();
mean = 2;
for (int i = 0; i < numSamples; ++i)
{
rs.Push(SimpleRNG.GetExponential(mean));
}
PrintResults("exponential", mean, 5, rs.Mean(), rs.Variance());
// Gamma distribution
rs.Clear();
shape = 10; scale = 2;
for (int i = 0; i < numSamples; ++i)
{
rs.Push(SimpleRNG.GetGamma(shape, scale));
}
PrintResults("gamma", shape * scale, shape * scale * scale, rs.Mean(), rs.Variance());
// Normal distribution
rs.Clear();
mean = 2; stdev = 5;
for (int i = 0; i < numSamples; ++i)
{
rs.Push(SimpleRNG.GetNormal(2, 5));
}
PrintResults("normal", mean, stdev * stdev, rs.Mean(), rs.Variance());
// Student t distribution
rs.Clear();
degreesOfFreedom = 6;
for (int i = 0; i < numSamples; ++i)
{
rs.Push(SimpleRNG.GetStudentT(6));
}
PrintResults("Student t", 0, degreesOfFreedom / (degreesOfFreedom - 2.0), rs.Mean(), rs.Variance());
// Weibull distribution
rs.Clear();
shape = 2; scale = 3;
mean = 3 * Math.Sqrt(Math.PI) / 2;
variance = 9 * (1 - Math.PI / 4);
for (int i = 0; i < numSamples; ++i)
{
rs.Push(SimpleRNG.GetWeibull(shape, scale));
}
PrintResults("Weibull", mean, variance, rs.Mean(), rs.Variance());
// Beta distribution
rs.Clear();
double a = 7, b = 2;
mean = a / (a + b);
variance = mean * (1 - mean) / (a + b + 1);
for (int i = 0; i < numSamples; ++i)
{
rs.Push(SimpleRNG.GetBeta(a, b));
}
PrintResults("Beta", mean, variance, rs.Mean(), rs.Variance());
}
