  Length of hospital stay (LOS) is an important indicator of the hospital
activity and management of health care. The skewness in the distribution of LOS
poses problems in statistical modelling because it fails to adequately follow
the usual traditional distribution such as the log-normal distribution. The aim
of this work is to model the variable LOS using the convolution of two
distributions; a technique well known in the signal processing community. The
specificity of that model is that the variable of interest is considered to be
the resulting sum of two random variables with different distributions. One of
the variables will feature the patient-related factors in terms their need to
recover from their admission condition, while the other models the hospital
management process such as the discharging process. Two estimation procedures
are proposed. One is the classical maximum likelihood, while the other relates
to the expectation maximisation algorithm. We will present some results
obtained by applying this model to a set of real data from a group of hospitals
in Victoria (Australia).
