public void ConstructorTest2()
{
var normal = SkewNormalDistribution.Normal(mean: 4, stdDev: 4.2);
double mean = normal.Mean; // 4.0
double median = normal.Median; // 4.0
double var = normal.Variance; // 17.64
double mode = normal.Mode; // 4.0
double cdf = normal.DistributionFunction(x: 1.4); // 0.26794249453351904
double pdf = normal.ProbabilityDensityFunction(x: 1.4); // 0.078423391448155175
double lpdf = normal.LogProbabilityDensityFunction(x: 1.4); // -2.5456330358182586
double ccdf = normal.ComplementaryDistributionFunction(x: 1.4); // 0.732057505466481
double icdf = normal.InverseDistributionFunction(p: cdf); // 1.4
double hf = normal.HazardFunction(x: 1.4); // 0.10712736480747137
double chf = normal.CumulativeHazardFunction(x: 1.4); // 0.31189620872601354
string str = normal.ToString(CultureInfo.InvariantCulture); // Sn(x; ξ = 4, ω = 4.2, α = 0)
Assert.AreEqual(4.0, mean);
Assert.AreEqual(4.0, median, 1e-5);
Assert.AreEqual(17.64, var);
Assert.AreEqual(4, mode, 1e-6);
Assert.AreEqual(0.31189620872601354, chf);
Assert.AreEqual(0.26794249453351904, cdf);
Assert.AreEqual(0.078423391448155175, pdf, 1e-8);
Assert.AreEqual(-2.5456330358182586, lpdf, 1e-8);
Assert.AreEqual(0.10712736480747137, hf, 1e-8);
Assert.AreEqual(0.732057505466481, ccdf, 1e-8);
Assert.AreEqual(1.4, icdf, 1e-8);
Assert.AreEqual("Sn(x; ξ = 4, ω = 4.2, α = 0)", str);
}
public void ConstructorTest1()
{
// Create a Skew normal distribution with location 2, scale 3 and shape 4.2
var skewNormal = new SkewNormalDistribution(location: 2, scale: 3, shape: 4.2);
double mean = skewNormal.Mean; // 4.3285611780515953
double median = skewNormal.Median; // 4.0230040653062265
double var = skewNormal.Variance; // 3.5778028400709641
double mode = skewNormal.Mode; // 3.220622226764422
double cdf = skewNormal.DistributionFunction(x: 1.4); // 0.020166854942526125
double pdf = skewNormal.ProbabilityDensityFunction(x: 1.4); // 0.052257431834162059
double lpdf = skewNormal.LogProbabilityDensityFunction(x: 1.4); // -2.9515731621912877
double ccdf = skewNormal.ComplementaryDistributionFunction(x: 1.4); // 0.97983314505747388
double icdf = skewNormal.InverseDistributionFunction(p: cdf); // 1.3999998597203041
double hf = skewNormal.HazardFunction(x: 1.4); // 0.053332990517581239
double chf = skewNormal.CumulativeHazardFunction(x: 1.4); // 0.020372981958858238
string str = skewNormal.ToString(CultureInfo.InvariantCulture); // Sn(x; ξ = 2, ω = 3, α = 4.2)
Assert.AreEqual(4.3285611780515953, mean);
Assert.AreEqual(4.0230040653062265, median);
Assert.AreEqual(3.2206222267273086, mode);
Assert.AreEqual(3.5778028400709641, var);
Assert.AreEqual(0.020372981958858238, chf);
Assert.AreEqual(0.020166854942526125, cdf);
Assert.AreEqual(0.052257431834161927, pdf);
Assert.AreEqual(-2.9515731621912908, lpdf);
Assert.AreEqual(0.053332990517581107, hf);
Assert.AreEqual(0.97983314505747388, ccdf);
Assert.AreEqual(1.3999998597203041, icdf);
Assert.AreEqual("Sn(x; ξ = 2, ω = 3, α = 4.2)", str);
}
private static SkewNormalDistribution MakeSkewNormalDistribution(decimal location, decimal median, decimal dispersion, decimal skew)
{
SkewNormalDistribution distribution = new SkewNormalDistribution(
(double)location,
(double)(median * dispersion),
(double)skew);
return(distribution);
}
public decimal ComputeProbabilityAboveX(InputGraphSelection selection, decimal x)
{
decimal location = FindDistributionLocation(selection.Median, selection.Dispersion, selection.Skew);
SkewNormalDistribution distribution = MakeSkewNormalDistribution(
location,
selection.Median,
selection.Dispersion,
selection.Skew);
decimal max = location * 100m;
return((decimal)(distribution.DistributionFunction((double)max) - distribution.DistributionFunction((double)x)));
}
private static decimal FindDistributionLocation(decimal median, decimal dispersion, decimal skew)
{
decimal location;
decimal acceptableRange = median / 50;
if (skew == 0)
{
location = median;
}
else
{
Compare compare = value =>
{
SkewNormalDistribution distribution = MakeSkewNormalDistribution(
value,
median,
dispersion,
skew);
decimal distMedian = (decimal)distribution.Median;
int cmp;
if (Math.Abs(distMedian - median) < acceptableRange)
{
cmp = 0;
}
else if (distMedian > median)
{
cmp = -1;
}
else
{
cmp = 1;
}
return(cmp);
};
location = BinarySearch.Search(0, median * 5, compare);
}
return(location);
}
public PreparedDataPoints GenerateDataPoints(decimal median, decimal dispersion, decimal skew, decimal?maxXValue)
{
decimal maxGraph = median * maxGraphXAxisTimesMedian;
if (maxXValue.HasValue && maxXValue.Value < maxGraph)
{
maxGraph = maxXValue.Value;
}
decimal location = FindDistributionLocation(median, dispersion, skew);
SkewNormalDistribution distribution = MakeSkewNormalDistribution(
location,
median,
dispersion,
skew);
int numIntervals;
int step = FindGraphPercentageIntervals(median, maxGraph, out numIntervals);
string[] labels = new string[numIntervals];
List <decimal?> decimals = new List <decimal?>(numIntervals);
int startInterval = 0;
// Make sure not to include distribution data at negative x offset.
// This is due to normal distribution not appropriate in all cases
decimal xValue = startInterval * step;
decimal lastValue = (decimal)distribution.DistributionFunction((double)xValue);
for (int i = startInterval; i < numIntervals; ++i)
{
decimal computeXValue = xValue + step / 2m;
labels[i] = "" + xValue;
decimal distValue = (decimal)distribution.DistributionFunction((double)computeXValue);
xValue += step;
decimal fractionOfX = 1 / (decimal)numIntervals;
// ?? sometimes occurs, but not significant
decimal diff;
if (distValue <= lastValue)
{
diff = 0;
}
else
{
diff = distValue - lastValue;
lastValue = distValue;
}
decimals.Add(diff / fractionOfX);
}
DataSet dataSet = new DataSet(null, Color.Green, decimals);
return(new PreparedDataPoints(labels, new DataSet[] { dataSet }));
}
