public void DistributionFunctionTest()
{
// http://www.stat.yale.edu/Courses/1997-98/101/binom.htm
// Verified in http://stattrek.com/online-calculator/binomial.aspx
double[] pmf = { 0.0260838446329553, 0.10433562893683, 0.198238170750635, 0.237886375826923, 0.202203904741285 };
double[] cdfLess = { 0.0000000000000000, 0.0260838446329553, 0.130419473569785, 0.32865764432042, 0.566544020147343 };
double[] cdfLessEqual = { 0.0260838446329553, 0.130419473569785, 0.32865764432042, 0.566544020147343, 0.768747924888628 };
double[] cdfGreater = { 0.973916155367045, 0.869580526430215, 0.67134235567958, 0.433455979852657, 0.231252075111372 };
double[] cdfGreaterEqual = { 1.000000000000000, 0.973916155367045, 0.869580526430215, 0.67134235567958, 0.433455979852657 };
int trials = 20;
double probability = 0.166667;
BinomialDistribution target = new BinomialDistribution(trials, probability);
for (int i = 0; i < pmf.Length; i++)
{
{ // P(X = i)
double actual = target.ProbabilityMassFunction(i);
Assert.AreEqual(pmf[i], actual, 1e-4);
Assert.IsFalse(Double.IsNaN(actual));
}
{ // P(X <= i)
double actual = target.DistributionFunction(i);
Assert.AreEqual(cdfLessEqual[i], actual, 1e-4);
Assert.IsFalse(Double.IsNaN(actual));
}
{ // P(X < i)
double actual = target.DistributionFunction(i, inclusive: false);
Assert.AreEqual(cdfLess[i], actual, 1e-4);
Assert.IsFalse(Double.IsNaN(actual));
}
{ // P(X > i)
double actual = target.ComplementaryDistributionFunction(i);
Assert.AreEqual(cdfGreater[i], actual, 1e-4);
Assert.IsFalse(Double.IsNaN(actual));
}
{ // P(X >= i)
double actual = target.ComplementaryDistributionFunction(i, inclusive: true);
Assert.AreEqual(cdfGreaterEqual[i], actual, 1e-4);
Assert.IsFalse(Double.IsNaN(actual));
}
}
}
public void ConstructorTest()
{
var bin = new BinomialDistribution(trials: 16, probability: 0.12);
double mean = bin.Mean; // 1.92
double median = bin.Median; // 2
double var = bin.Variance; // 1.6896
double mode = bin.Mode; // 2
double cdf = bin.DistributionFunction(k: 0); // 0.12933699143209909
double pdf = bin.ProbabilityMassFunction(k: 1); // 0.28218979948821621
double lpdf = bin.LogProbabilityMassFunction(k: 0); // -2.0453339441581582
double ccdf = bin.ComplementaryDistributionFunction(k: 0); // 0.87066300856790091
int icdf0 = bin.InverseDistributionFunction(p: 0.37); // 1
int icdf1 = bin.InverseDistributionFunction(p: 0.50); // 2
int icdf2 = bin.InverseDistributionFunction(p: 0.99); // 5
int icdf3 = bin.InverseDistributionFunction(p: 0.999); // 7
double hf = bin.HazardFunction(x: 0); // 1.3809523809523814
double chf = bin.CumulativeHazardFunction(x: 0); // 0.86750056770472328
string str = bin.ToString(CultureInfo.InvariantCulture); // "Binomial(x; n = 16, p = 0.12)"
double[] probabilities = new double[10];
for (int i = 0; i < probabilities.Length; i++)
{
probabilities[i] = bin.ProbabilityMassFunction(i);
}
Assert.AreEqual(1.92, mean);
Assert.AreEqual(2, median);
Assert.AreEqual(2, mode);
Assert.AreEqual(1.6896, var);
Assert.AreEqual(0.13850027875444251, chf, 1e-10);
Assert.AreEqual(0.12933699143209909, cdf, 1e-10);
Assert.AreEqual(0.28218979948821621, pdf, 1e-10);
Assert.AreEqual(-2.0453339441581582, lpdf);
Assert.AreEqual(0.14855000173354949, hf, 1e-10);
Assert.AreEqual(0.87066300856790091, ccdf, 1e-10);
Assert.AreEqual(1, icdf0);
Assert.AreEqual(2, icdf1);
Assert.AreEqual(5, icdf2);
Assert.AreEqual(7, icdf3);
Assert.AreEqual("Binomial(x; n = 16, p = 0.12)", str);
var range1 = bin.GetRange(0.95);
var range2 = bin.GetRange(0.99);
var range3 = bin.GetRange(0.01);
Assert.AreEqual(0.0, range1.Min);
Assert.AreEqual(4.0, range1.Max);
Assert.AreEqual(0.0, range2.Min);
Assert.AreEqual(5.0, range2.Max);
Assert.AreEqual(0.0, range3.Min);
Assert.AreEqual(5.0, range3.Max);
}
public void ConstructorTest()
{
var bin = new BinomialDistribution(trials: 16, probability: 0.12);
double mean = bin.Mean; // 1.92
double median = bin.Median; // 2
double var = bin.Variance; // 1.6896
double mode = bin.Mode; // 2
double cdf = bin.DistributionFunction(k: 0); // 0.12933699143209909
double pdf = bin.ProbabilityMassFunction(k: 1); // 0.28218979948821621
double lpdf = bin.LogProbabilityMassFunction(k: 0); // -2.0453339441581582
double ccdf = bin.ComplementaryDistributionFunction(k: 0); // 0.87066300856790091
int icdf0 = bin.InverseDistributionFunction(p: 0.37); // 1
int icdf1 = bin.InverseDistributionFunction(p: 0.50); // 2
int icdf2 = bin.InverseDistributionFunction(p: 0.99); // 5
int icdf3 = bin.InverseDistributionFunction(p: 0.999); // 7
double hf = bin.HazardFunction(x: 0); // 1.3809523809523814
double chf = bin.CumulativeHazardFunction(x: 0); // 0.86750056770472328
string str = bin.ToString(CultureInfo.InvariantCulture); // "Binomial(x; n = 16, p = 0.12)"
double[] probabilities = new double[10];
for (int i = 0; i < probabilities.Length; i++)
probabilities[i] = bin.ProbabilityMassFunction(i);
Assert.AreEqual(1.92, mean);
Assert.AreEqual(2, median);
Assert.AreEqual(2, mode);
Assert.AreEqual(1.6896, var);
Assert.AreEqual(0.13850027875444251, chf, 1e-10);
Assert.AreEqual(0.12933699143209909, cdf, 1e-10);
Assert.AreEqual(0.28218979948821621, pdf, 1e-10);
Assert.AreEqual(-2.0453339441581582, lpdf);
Assert.AreEqual(0.14855000173354949, hf, 1e-10);
Assert.AreEqual(0.87066300856790091, ccdf, 1e-10);
Assert.AreEqual(1, icdf0);
Assert.AreEqual(2, icdf1);
Assert.AreEqual(5, icdf2);
Assert.AreEqual(7, icdf3);
Assert.AreEqual("Binomial(x; n = 16, p = 0.12)", str);
var range1 = bin.GetRange(0.95);
var range2 = bin.GetRange(0.99);
var range3 = bin.GetRange(0.01);
Assert.AreEqual(0.0, range1.Min);
Assert.AreEqual(4.0, range1.Max);
Assert.AreEqual(0.0, range2.Min);
Assert.AreEqual(5.0, range2.Max);
Assert.AreEqual(0.0, range3.Min);
Assert.AreEqual(5.0, range3.Max);
}
public void DistributionFunctionTest()
{
// http://www.stat.yale.edu/Courses/1997-98/101/binom.htm
// Verified in http://stattrek.com/online-calculator/binomial.aspx
double[] pmf = { 0.0260838446329553, 0.10433562893683, 0.198238170750635, 0.237886375826923, 0.202203904741285 };
double[] cdfLess = { 0.0000000000000000, 0.0260838446329553, 0.130419473569785, 0.32865764432042, 0.566544020147343 };
double[] cdfLessEqual = { 0.0260838446329553, 0.130419473569785, 0.32865764432042, 0.566544020147343, 0.768747924888628 };
double[] cdfGreater = { 0.973916155367045, 0.869580526430215, 0.67134235567958, 0.433455979852657, 0.231252075111372 };
double[] cdfGreaterEqual = { 1.000000000000000, 0.973916155367045, 0.869580526430215, 0.67134235567958, 0.433455979852657 };
int trials = 20;
double probability = 0.166667;
BinomialDistribution target = new BinomialDistribution(trials, probability);
for (int i = 0; i < pmf.Length; i++)
{
{ // P(X = i)
double actual = target.ProbabilityMassFunction(i);
Assert.AreEqual(pmf[i], actual, 1e-4);
Assert.IsFalse(Double.IsNaN(actual));
}
{ // P(X <= i)
double actual = target.DistributionFunction(i);
Assert.AreEqual(cdfLessEqual[i], actual, 1e-4);
Assert.IsFalse(Double.IsNaN(actual));
}
{ // P(X < i)
double actual = target.DistributionFunction(i, inclusive: false);
Assert.AreEqual(cdfLess[i], actual, 1e-4);
Assert.IsFalse(Double.IsNaN(actual));
}
{ // P(X > i)
double actual = target.ComplementaryDistributionFunction(i);
Assert.AreEqual(cdfGreater[i], actual, 1e-4);
Assert.IsFalse(Double.IsNaN(actual));
}
{ // P(X >= i)
double actual = target.ComplementaryDistributionFunction(i, inclusive: true);
Assert.AreEqual(cdfGreaterEqual[i], actual, 1e-4);
Assert.IsFalse(Double.IsNaN(actual));
}
}
}