/// <summary>
/// The expected logarithm of that distribution under this distribution.
/// </summary>
/// <param name="that">The distribution to take the logarithm of.</param>
/// <returns><c>sum_x this.Evaluate(x)*Math.Log(that.Evaluate(x))</c></returns>
/// <remarks>This is also known as the cross entropy.</remarks>
public double GetAverageLog(GammaPower that)
{
if (that.IsPointMass)
{
if (this.IsPointMass && this.Point.Equals(that.Point))
{
return(0.0);
}
else
{
return(Double.NegativeInfinity);
}
}
else if (!IsProper())
{
throw new ImproperDistributionException(this);
}
else
{
// that is not a point mass.
double invPower = 1.0 / that.Power;
double result = (that.Shape * invPower - 1) * GetMeanLog() - GetMeanPower(invPower) * that.Rate;
result -= that.GetLogNormalizer();
return(result);
}
}
/// <summary>
/// The log of the integral of the product of this Gamma and that Gamma
/// </summary>
/// <param name="that">That Gamma</param>
/// <returns>The log inner product</returns>
public double GetLogAverageOf(GammaPower that)
{
if (IsPointMass)
{
return(that.GetLogProb(Point));
}
else if (that.IsPointMass)
{
return(GetLogProb(that.Point));
}
else
{
GammaPower product = this * that;
//if (!product.IsProper()) throw new ArgumentException("The product is improper");
return(product.GetLogNormalizer() - this.GetLogNormalizer() - that.GetLogNormalizer());
}
}
/// <summary>
/// Get the integral of this distribution times another distribution raised to a power.
/// </summary>
/// <param name="that"></param>
/// <param name="power"></param>
/// <returns></returns>
public double GetLogAverageOfPower(GammaPower that, double power)
{
if (IsPointMass)
{
return(power * that.GetLogProb(Point));
}
else if (that.IsPointMass)
{
if (power < 0)
{
throw new DivideByZeroException("The exponent is negative and the distribution is a point mass");
}
return(this.GetLogProb(that.Point));
}
else
{
var product = this * (that ^ power);
return(product.GetLogNormalizer() - this.GetLogNormalizer() - power * that.GetLogNormalizer());
}
}
