Appendix

The gamma distribution is widely used in different appliied fields of probability theory. It has the probability density

γα,β(t) = 1

βαΓ(α) exp

( − t β

) tα−1

for t ≥ 0 and α, β > 0. Basic summary statistics for a gamma distributed random variable X are

• E[X] = αβ • V[X] = αβ2

• γα,β(tmax) != max for tmax = β(α− 1). The parameter α can be interpreted as a shape parameter, whereas the second parameter β can be considered as a scale parameter. Special gamma distributions include the

• Erlang distribution in case of α ∈ N • Exponential distribution in case of α = 1 • Chi-squared distribution with n degrees of freedom in case of α = n/2 and n ∈ N.