I am working on the use of distributed delay applied to pharmacometric models. Specifically, the delay kernel I am interested in is the Gamma distribution, with non-integer shape.
The historical values $y$ are a simple table of values at points in time.
Calculation of a distributed delay requires convolving the Gamma distribution with the $y(t)$ function.
I have done this by modeling $y(t)$ as a series of rectangles, and the convolution with each rectangle is very simple, using the CDF of Gamma.
However, it would be more accurate if I could treat $y(t)$ as a series of trapezoids. I could do this if I could find an expression for the convolution of the Gamma with a simple right triangle distribution, but my math skills are not up to the task.
Does anyone know how to do this, or can point me to a good reference?