I know that the gamma distribution with parameters $k$ and $\theta$ can be used as a model for the occurrence of events. The requirement on the events would be that their occurrence is random and the mean time between them equals $\theta$ and that they belong to a Poisson process.
Now I have a question regarding the applicability of these:
I want to model a biological growth process where we think of the resulting length as random. What we do know is that the underlying processes (biochemical etc.) are Poisson processes. Is it in the context of the statement above appropriate to model the length with a gamma random variable?