Modeling Phone Call Durations via Switching Poisson Processes with Applications in Mental Health

This work models phone call durations via switching Poisson point processes. This kind of processes is composed by two intertwined intensity functions: one models the start of a call, whereas the other one models when the call ends. Thus, the call duration is obtained from the inverse of the intensity function of finishing a call. Additionally, to model the circadian rhythm present in human behavior, we shall use a (pos-itive) truncated Fourier series as the parametric form of the intensities. Finally, the maximum likelihood estimates of the intensity functions are obtained using a trust region method and the performance is evaluated on synthetic and real data, showing good results.