public void ValidateInverseCumulativeDistribution(double lambda, double x)
{
var n = new Exponential(lambda);
Assert.AreEqual(x, n.InverseCumulativeDistribution(1.0 - Math.Exp(-lambda * x)));
Assert.AreEqual(x, Exponential.InvCDF(lambda, 1.0 - Math.Exp(-lambda * x)));
}
public Position1 Sample(Random random)
{
Position1 distance = Domain.Entry + (float)distribution.InverseCumulativeDistribution(random.NextDouble());
if (float.IsNaN(distance))
{
throw new InvalidOperationException($"Exponential distribution returned invalid distance {distance}");
}
return(distance <= Domain.Exit ? distance : Position1.PositiveInfinity);
}
public static void TestGEVLocation()
{
//var dist = new Normal(0, 1, Program.rand);
var dist = new Exponential(2, Program.rand);
double estimateLoc(int n) => Math.Sqrt(2 * Math.Log(n) - Math.Log(Math.Log(n)) - Math.Log(4 * Math.PI));
for (int n = 150; n < 500; n += 10)
{
double proportion = (n - 0.78) / n;
double quant = dist.InverseCumulativeDistribution(proportion);
double estimate = estimateLoc(n);
//Console.WriteLine($"Quantile: {quant} Est: {estimate} Error: {Math.Abs(estimate - quant)}");
var props = Interpolation.Linspace(0.000000001, 0.999999999, 10000);
var quants = new double[10000];
for (int i = 0; i < quants.Length; i++)
{
quants[i] = dist.InverseCumulativeDistribution(props[i]);
}
GPDApproximation.ApproximateExcessDistributionParametersV4(quants, out double a, out double c, out double u);
var tailApprox = new GPDApproximation(quants, GPDApproximation.FittingMethod.V4);
var sample = new double[10000];
for (int i = 0; i < 10000; i++)
{
double max = 0;
for (int j = 0; j < n; j++)
{
max = Math.Max(max, tailApprox.Sample());
}
sample[i] = max;
}
double shapeGuess = tailApprox.c;
double g1 = SpecialFunctions.Gamma(1 - shapeGuess);
double g2 = SpecialFunctions.Gamma(1 - 2 * shapeGuess);
double scaleGuess = Math.Sqrt(Statistics.Variance(sample) * shapeGuess * shapeGuess / (g2 - g1 * g1));
double locationGuess = Statistics.Mean(sample) - scaleGuess * (g1 - 1) / shapeGuess;
Console.WriteLine($"Quantile: {quant} IntroEst: {estimate} Error: {Math.Abs(estimate - quant)} Bootstrap:{locationGuess} Shape {shapeGuess}");
}
}
public double InverseCumulativeDistribution(double p)
{
return(exponential.InverseCumulativeDistribution(p));
}