public static void DistributionMoments()
{
//ContinuousDistribution d = new GumbelDistribution();
DiscreteDistribution d = new PoissonDistribution(5);
Console.WriteLine($"support = {d.Support}");
Console.WriteLine($"mean = {d.Mean}");
Console.WriteLine($"mean as expectation = {d.ExpectationValue(x => x)}");
Console.WriteLine($"variance = {d.Variance}");
Console.WriteLine($"variance as expectation = {d.ExpectationValue(x => MoreMath.Sqr(x - d.Mean))}");
Console.WriteLine($"standard deviation = {d.StandardDeviation}");
Console.WriteLine($"skewness = {d.Skewness}");
Console.WriteLine($"excess kuritosis = {d.ExcessKurtosis}");
for (int r = 0; r <= 4; r++)
{
Console.WriteLine($"M_{r} = {d.RawMoment(r)}");
Console.WriteLine($"C_{r} = {d.CentralMoment(r)}");
Console.WriteLine($"K_{r} = {d.Cumulant(r)}");
}
}
