public TruncatedDistribution(ITruncatableDistribution <double> distribution, double lowerBound, double upperBound)
{
if (lowerBound > upperBound)
{
throw new ArgumentOutOfRangeException($"lowerBound ({lowerBound}) > upperBound ({upperBound})");
}
this.Distribution = distribution;
this.LowerBound = lowerBound;
this.UpperBound = upperBound;
this.TotalProbability = distribution.GetProbBetween(lowerBound, upperBound);
this.LowerProbability = distribution.GetProbLessThan(lowerBound);
}
/// <summary>
/// Returns the integral from lowerBound to upperBound of func(x) times p(x).
/// </summary>
public static double Integral(double lowerBound, double upperBound, Func <double, double> func, ITruncatableDistribution <double> distribution)
{
var dist = new TruncatedDistribution(distribution, lowerBound, upperBound);
// To approximate the average, we divide the region into intervals of equal probability.
// We compute the function at the midpoint of each interval, and take an unweighted average.
// The quantile ranks of the midpoints are 0.5/count, 1.5/count, ..., (count-0.5)/count
const int count = 100;
double increment = 1.0 / count;
double start = increment / 2;
double sum = 0;
for (int i = 0; i < count; i++)
{
double quantileRank = start + i * increment;
double input = dist.GetQuantile(quantileRank);
sum += func(input);
}
return(sum * increment * distribution.GetProbBetween(lowerBound, upperBound));
}
/// <inheritdoc/>
public double GetProbBetween(double lowerBound, double upperBound)
{
lowerBound = Math.Min(UpperBound, Math.Max(LowerBound, lowerBound));
upperBound = Math.Min(UpperBound, Math.Max(LowerBound, upperBound));
return(Distribution.GetProbBetween(lowerBound, upperBound) / TotalProbability);
}