// Helper functions
private static double ComputeDensityEstimation(double pickupDelay, double duration, double interval, IEnumerable <Leg> legs)
{
MultivariateEmpiricalDistribution dist = new MultivariateEmpiricalDistribution(legs
.Where(l => l.NumOfPassengersPickedUp > 0)
.Select(l => (new double[] {
GetPickupDelay(l),
l.ArrivalTime.Subtract(l.StartTime).TotalMinutes
})).ToArray());
double probDist = 1 - dist.DistributionFunction(new double[] { pickupDelay, duration });
// compute appropriate univariate distribution
if (Math.Abs(dist.Variance[0]) < Double.Epsilon)
{
dist = new MultivariateEmpiricalDistribution(legs
.Where(l => l.NumOfPassengersPickedUp > 0)
.Select(l => (new double[] {
l.ArrivalTime.Subtract(l.StartTime).TotalMinutes
})).ToArray());
probDist = 1 - dist.DistributionFunction(new double[] { duration });
}
double frequency = legs.Count(l => Math.Abs(l.StartTime.Subtract(DateTime.Now).TotalDays) < 2 &&
l.NumOfPassengersPickedUp > 0) / 5760.0;
return(probDist * frequency * interval);
}
public void WeightedEmpiricalDistributionConstructorTest2()
{
double[] original = { 5, 5, 1, 4, 1, 2, 2, 3, 3, 3, 4, 3, 3, 3, 4, 3, 2, 3 };
var distribution = new MultivariateEmpiricalDistribution(original.ToArray());
double[] weights = { 2, 1, 1, 1, 2, 3, 1, 3, 1, 1, 1, 1 };
double[] source = { 5, 1, 4, 1, 2, 3, 4, 3, 4, 3, 2, 3 };
double[][] samples = source.ToArray();
weights = weights.Divide(weights.Sum());
var target = new MultivariateEmpiricalDistribution(samples,
weights, distribution.Smoothing);
Assert.AreEqual(distribution.Mean[0], target.Mean[0]);
Assert.AreEqual(distribution.Median[0], target.Median[0]);
Assert.AreEqual(distribution.Mode[0], target.Mode[0]);
Assert.AreEqual(distribution.Smoothing[0, 0], target.Smoothing[0, 0]);
Assert.AreEqual(1.3655172413793104, target.Variance[0]);
Assert.AreEqual(target.Weights, weights);
Assert.AreEqual(target.Samples, samples);
for (double x = 0; x < 6; x += 0.1)
{
double actual, expected;
expected = distribution.ComplementaryDistributionFunction(x);
actual = target.ComplementaryDistributionFunction(x);
Assert.AreEqual(expected, actual, 1e-15);
expected = distribution.DistributionFunction(x);
actual = target.DistributionFunction(x);
Assert.AreEqual(expected, actual, 1e-15);
expected = distribution.LogProbabilityDensityFunction(x);
actual = target.LogProbabilityDensityFunction(x);
Assert.AreEqual(expected, actual, 1e-15);
expected = distribution.ProbabilityDensityFunction(x);
actual = target.ProbabilityDensityFunction(x);
Assert.AreEqual(expected, actual, 1e-15);
}
}
public void FitTest()
{
double[] original = { 5, 5, 1, 4, 1, 2, 2, 3, 3, 3, 4, 3, 3, 3, 4, 3, 2, 3 };
var distribution = new MultivariateEmpiricalDistribution(original.ToJagged());
int[] weights = { 2, 1, 1, 1, 2, 3, 1, 3, 1, 1, 1, 1 };
double[] sources = { 5, 1, 4, 1, 2, 3, 4, 3, 4, 3, 2, 3 };
double[][] samples = sources.ToJagged();
var target = new MultivariateEmpiricalDistribution(Jagged.Zeros(1, 1));
target.Fit(samples, weights);
Assert.AreEqual(distribution.Mean[0], target.Mean[0]);
Assert.AreEqual(distribution.Median[0], target.Median[0]);
Assert.AreEqual(distribution.Mode[0], target.Mode[0]);
Assert.AreEqual(distribution.Smoothing[0, 0], target.Smoothing[0, 0]);
Assert.AreEqual(distribution.Variance[0], target.Variance[0]);
Assert.IsTrue(target.Weights.IsEqual(weights.Divide(weights.Sum())));
Assert.AreEqual(target.Samples, samples);
for (double x = 0; x < 6; x += 0.1)
{
double actual, expected;
expected = distribution.ComplementaryDistributionFunction(x);
actual = target.ComplementaryDistributionFunction(x);
Assert.AreEqual(expected, actual);
expected = distribution.DistributionFunction(x);
actual = target.DistributionFunction(x);
Assert.AreEqual(expected, actual);
expected = distribution.LogProbabilityDensityFunction(x);
actual = target.LogProbabilityDensityFunction(x);
Assert.AreEqual(expected, actual, 1e-15);
expected = distribution.ProbabilityDensityFunction(x);
actual = target.ProbabilityDensityFunction(x);
Assert.AreEqual(expected, actual, 1e-15);
}
}
public void WeightedEmpiricalDistribution_DistributionFunction()
{
double[][] samples =
{
new double[] { 5, 2 },
new double[] { 1, 5 },
new double[] { 4, 7 },
new double[] { 1, 6 },
new double[] { 2, 2 },
new double[] { 3, 4 },
new double[] { 4, 8 },
new double[] { 3, 2 },
new double[] { 4, 4 },
new double[] { 3, 7 },
new double[] { 2, 4 },
new double[] { 3, 1 },
};
var target = new MultivariateEmpiricalDistribution(samples);
double[] expected =
{
0.33333333333333331, 0.083333333333333329, 0.83333333333333337,
0.16666666666666666, 0.083333333333333329, 0.41666666666666669,
0.91666666666666663, 0.25, 0.5,
0.66666666666666663, 0.16666666666666666, 0.083333333333333329
};
for (int i = 0; i < samples.Length; i++)
{
double e = expected[i];
double a = target.DistributionFunction(samples[i]);
Assert.AreEqual(e, a);
}
}
