/// <summary>
/// Sets the parameters to represent the ratio of two Gammas
/// </summary>
/// <param name="numerator">The numerator Gamma. Can be the same object as this.</param>
/// <param name="denominator">The denominator Gamma. Can be the same object as this.</param>
/// <param name="forceProper">If true, the result has shape >= 1 and rate >= 0, under the constraint that result*denominator has the same mean as numerator</param>
public void SetToRatio(Gamma numerator, Gamma denominator, bool forceProper = false)
{
if (numerator.IsPointMass)
{
if (denominator.IsPointMass)
{
if (numerator.Point.Equals(denominator.Point))
{
SetToUniform();
}
else
{
throw new DivideByZeroException();
}
}
else
{
Point = numerator.Point;
}
}
else if (denominator.IsPointMass)
{
throw new DivideByZeroException();
}
else if (forceProper && numerator.Rate == 0)
{
Rate = 0;
Shape = 1 + Math.Max(0, numerator.Shape - denominator.Shape);
}
else if (forceProper && (numerator.Shape < denominator.Shape || numerator.Rate < denominator.Rate))
{
double mean = numerator.GetMean();
double shape = mean * denominator.Rate + (1 - denominator.Shape);
if (shape < 1)
{
Rate = denominator.Shape / mean - denominator.Rate;
Shape = 1;
}
else
{
Shape = shape;
Rate = 0;
}
}
else
{
if (Math.Abs(denominator.Shape) > 10)
{
Shape = (numerator.Shape - denominator.Shape) + 1;
}
else
{
// avoid roundoff errors when numerator shape is below eps
Shape = numerator.Shape + (1 - denominator.Shape);
}
Rate = numerator.Rate - denominator.Rate;
}
}
/// <summary>
/// Sets the parameters to represent the product of two Gammas.
/// </summary>
/// <param name="a">The first Gamma</param>
/// <param name="b">The second Gamma</param>
/// <remarks>
/// The result may not be proper. No error is thrown in this case.
/// </remarks>
public void SetToProduct(Gamma a, Gamma b)
{
if (a.IsPointMass)
{
if (b.IsPointMass && !a.Point.Equals(b.Point))
{
throw new AllZeroException();
}
Point = a.Point;
return;
}
else if (b.IsPointMass)
{
Point = b.Point;
return;
}
else
{
// avoid roundoff errors when a shape is below eps
if (a.Shape < b.Shape)
{
Shape = a.Shape + (b.Shape - 1);
}
else
{
Shape = b.Shape + (a.Shape - 1);
}
Rate = a.Rate + b.Rate;
if (Shape > double.MaxValue || Rate > double.MaxValue)
{
// (as + bs - 1)/(ar + br) = (am*ar + bm*br - 1)/(ar + br) = am*w + bm*(1-w) - 1/(ar + br)
// w = ar/(ar + br)
double w = 1 / (1 + b.Rate / a.Rate);
Point = a.GetMean() * w + b.GetMean() * (1 - w) - 1 / Rate;
}
}
}
