public void BetaMeanTest3()
{
int trials = 100;
int successes = 78;
BetaDistribution betaDistribution = new BetaDistribution(successes, trials);
double mean = betaDistribution.Mean; // 0.77450980392156865
double median = betaDistribution.Median; // 0.77630912598534851
double p025 = betaDistribution.InverseDistributionFunction(p: 0.025); // 0.68899653915764347
double p975 = betaDistribution.InverseDistributionFunction(p: 0.975); // 0.84983461640764513
double orig025 = betaDistribution.DistributionFunction(p025);
double orig975 = betaDistribution.DistributionFunction(p975);
Assert.AreEqual(0.025, orig025, 1e-8);
Assert.AreEqual(0.975, orig975, 1e-8);
Assert.AreEqual(0.77450980392156865, mean, 1e-9);
Assert.AreEqual(0.7763091275412235, median, 1e-9);
Assert.AreEqual(0.68899667463246894, p025, 1e-6);
Assert.AreEqual(0.84983461640764513, p975, 1e-6);
}