Accord.Statistics.Distributions.Univariate.NegativeBinomialDistribution.DistributionFunction C# (CSharp) Method

        public override double DistributionFunction(int k)
        {
            if (k < 0) 
                return 0;

            if (k == int.MaxValue)
                return 1;

            return 1.0 - Beta.Incomplete(k + 1, r, p);
        }

        public void ConstructorTest()
        {
            // Create a Negative Binomial distribution with r = 7, p = 0.42
            var dist = new NegativeBinomialDistribution(failures: 7, probability: 0.42);

            // Common measures
            double mean = dist.Mean;     // 5.068965517241379
            double median = dist.Median; // 5.0
            double var = dist.Variance;  // 8.7395957193816862

            // Cumulative distribution functions
            double cdf = dist.DistributionFunction(k: 2);               // 0.19605133020527743
            double ccdf = dist.ComplementaryDistributionFunction(k: 2); // 0.80394866979472257

            // Probability mass functions
            double pmf1 = dist.ProbabilityMassFunction(k: 4); // 0.054786846293416853
            double pmf2 = dist.ProbabilityMassFunction(k: 5); // 0.069908015870399909
            double pmf3 = dist.ProbabilityMassFunction(k: 6); // 0.0810932984096639
            double lpmf = dist.LogProbabilityMassFunction(k: 2); // -2.3927801721315989

            // Quantile function
            int icdf1 = dist.InverseDistributionFunction(p: 0.17); // 2
            int icdf2 = dist.InverseDistributionFunction(p: 0.46); // 4
            int icdf3 = dist.InverseDistributionFunction(p: 0.87); // 8

            // Hazard (failure rate) functions
            double hf = dist.HazardFunction(x: 4); // 0.10490438293398294
            double chf = dist.CumulativeHazardFunction(x: 4); // 0.64959916255036043

            // String representation
            string str = dist.ToString(CultureInfo.InvariantCulture); // "NegativeBinomial(x; r = 7, p = 0.42)"

            Assert.AreEqual(5.068965517241379, mean);
            Assert.AreEqual(5.0, median);
            Assert.AreEqual(8.7395957193816862, var);
            Assert.AreEqual(0.64959916255036043, chf, 1e-10);
            Assert.AreEqual(0.19605133020527743, cdf);
            Assert.AreEqual(0.054786846293416853, pmf1);
            Assert.AreEqual(0.069908015870399909, pmf2);
            Assert.AreEqual(0.0810932984096639, pmf3);
            Assert.AreEqual(-3.8297538146412009, lpmf);
            Assert.AreEqual(0.10490438293398294, hf);
            Assert.AreEqual(0.80394866979472257, ccdf);
            Assert.AreEqual(2, icdf1);
            Assert.AreEqual(4, icdf2);
            Assert.AreEqual(8, icdf3);
            Assert.AreEqual("NegativeBinomial(x; r = 7, p = 0.42)", str);
        }