/// <summary>
/// Get the mean and variance after truncation.
/// </summary>
/// <param name="mean"></param>
/// <param name="variance"></param>
public void GetMeanAndVariance(out double mean, out double variance)
{
if (this.Gamma.IsPointMass)
{
mean = this.Gamma.Point;
variance = 0.0;
}
else if (!IsProper())
{
throw new ImproperDistributionException(this);
}
else
{
// Apply the recurrence GammaUpper(s+1,x,false) = s*GammaUpper(s,x,false) + x^s*exp(-x)
// Z = GammaUpper(s,r*l,false) - GammaUpper(s,r*u,false)
// E[x] = (GammaUpper(s+1,r*l,false) - GammaUpper(s+1,r*u,false))/r/Z
// = (s + ((r*l)^s*exp(-r*l) - (r*u)^s*exp(-r*u))/Z)/r
double rl = this.Gamma.Rate * LowerBound;
double ru = this.Gamma.Rate * UpperBound;
double m = this.Gamma.Shape / this.Gamma.Rate;
double offset, offset2;
if (ru > double.MaxValue)
{
double logZ = GetLogNormalizer();
if (logZ < double.MinValue)
{
mean = GetMode();
variance = 0.0;
return;
}
offset = Math.Exp(MMath.GammaUpperLogScale(this.Gamma.Shape, rl) - logZ);
offset2 = (rl - this.Gamma.Shape) / this.Gamma.Rate * offset;
}
else
{
// This fails when GammaUpperScale underflows to 0
double Z = GetNormalizer();
if (Z == 0)
{
mean = GetMode();
variance = 0.0;
return;
}
double gammaUpperScaleLower = MMath.GammaUpperScale(this.Gamma.Shape, rl);
double gammaUpperScaleUpper = MMath.GammaUpperScale(this.Gamma.Shape, ru);
offset = (gammaUpperScaleLower - gammaUpperScaleUpper) / Z;
offset2 = ((rl - this.Gamma.Shape) / this.Gamma.Rate * gammaUpperScaleLower - (ru - this.Gamma.Shape) / this.Gamma.Rate * gammaUpperScaleUpper) / Z;
}
if (rl == this.Gamma.Shape)
{
mean = LowerBound + offset / this.Gamma.Rate;
}
else
{
mean = (this.Gamma.Shape + offset) / this.Gamma.Rate;
if (mean < LowerBound)
{
mean = MMath.NextDouble(mean);
}
if (mean < LowerBound)
{
mean = MMath.NextDouble(mean);
}
}
if (mean > double.MaxValue)
{
variance = mean;
}
else
{
variance = (m + offset2 + (1 - offset) * offset / this.Gamma.Rate) / this.Gamma.Rate;
}
}
}