The MNO-PQRS poisson point process: Generating the next event time

We discuss the problem of generating the time of the next event of a nonhomogeneous Poisson process with an MNO-PQRS rate function. A PQRS function is piecewise quadratic. At every time point, an MNO-PQRS rate function is the maximum of zero and a piecewise-quadratic function. We take as given the three quadratic coefficients of every time interval. In addition, we take as given the time of the previous event. The problem is then to generate the time of the next event. We review thinning algorithms, but focus on presenting an efficient inverse-transformation algorithm that converts a single pseudorandom number to the next-event time.