On the self-similar distribution of the emergency ward arrivals time series

Hospital emergency arrivals are often modeled as Poisson processes because of the similarity of the problem to a telephone exchange model, i.e. applications that involve counting the number of times a random event occurs in a given time, where the interval between individual counts follows the exponential distribution. In this paper, we propose a statistical modeling of hospital emergency ward arrivals, using self-similar processes. This modeling takes into account the fact that it is known empirically that the emergency time series consists of periods marked by "bursts" of high level demand peaks, followed by periods of lower demand. This is explained neither by a Poisson during fixed-lengths intervals nor by a lognormal distribution. We show that a self-similar distribution can model this phenomenon. We also show that the commonly used Poisson models seriously underestimate the "burstiness" of emergency arrivals over a wide range of time scales, and that the emergency time series cannot be modeled by a lognormal distribution. The self-similar distribution was tested by the Hurst parameter, which we have calculated using five different methods, all of which agree on the value of the parameter.