public static void TestMean(IGaussianDistribution <double> dist)
{
int sampleCount = 10000000;
double sum = 0.0;
for (int i = 0; i < sampleCount; i++)
{
sum += dist.Sample();
}
double mean = sum / sampleCount;
Assert.IsTrue(Math.Abs(mean) < 0.001);
}
public static void TestSimpleStats(IGaussianDistribution <double> dist)
{
const int sampleCount = 20_000_000;
RunningStatistics runningStats = new RunningStatistics();
for (int i = 0; i < sampleCount; i++)
{
runningStats.Push(dist.Sample());
}
Assert.IsTrue(Math.Abs(runningStats.Mean) < 0.001);
Assert.IsTrue(Math.Abs(runningStats.StandardDeviation - 1.0) < 0.0005);
Assert.IsTrue(Math.Abs(runningStats.Skewness) < 0.01);
Assert.IsTrue(Math.Abs(runningStats.Kurtosis) < 0.01);
}
public static void TestStandardDeviation(IGaussianDistribution <double> dist)
{
int sampleCount = 10000000;
double sqrSum = 0.0;
for (int i = 0; i < sampleCount; i++)
{
double x = dist.Sample();
sqrSum += x * x;
}
double var = sqrSum / sampleCount;
double stdDev = Math.Sqrt(var);
Assert.IsTrue(Math.Abs(stdDev - 1.0) < 0.001);
}
public static void TestDistribution(IGaussianDistribution <double> dist, double mean, double stdDev)
{
// Take a set of samples.
const int sampleCount = 10_000_000;
double[] sampleArr = new double[sampleCount];
for (int i = 0; i < sampleCount; i++)
{
sampleArr[i] = dist.Sample();
}
// Sort the ample so that we can use SortedArrayStatistics.
Array.Sort(sampleArr);
//// Test a range of centile/quantile values.
double lowerBound = -5;
double upperBound = 5;
double tauStep = (upperBound - lowerBound) / 30.0;
for (double tau = 0; tau <= 1.0; tau += 0.1)
{
// Notes.
// Here we calc the tau'th quartile over a range of values in he interval [0,1],
// the resulting quantile is the sample value (and CDF x-axis value) at which the
// CDF crosses tau on the y-axis.
//
// We then take that sample x-axis value, pass it through the CDF function for the
// gaussian to obtain the expected y value at that x, and compare with tau.
// Determine the x value at which tau (as a proportion) of samples are <= x.
double sample_x = SortedArrayStatistics.Quantile(sampleArr, tau);
// Put sample_x into the gaussian CDF function, to obtain a CDF y coord..
double cdf_y = 0.5 * SpecialFunctions.Erfc((mean - sample_x) / (stdDev * Constants.Sqrt2));
// Compare the expected and actual CDF y values.
double y_error = Math.Abs(tau - cdf_y);
Assert.IsTrue(y_error < 0.0005);
}
}