Seasonal generalized exponential probability models with application to interstorm and storm durations

A simple generalization of the exponential probability model is presented which provides a flexible method for identifying and fitting probability distributions. When coupled with likelihood‐based estimation, this approach enables a parsimonious description of seasonal dependence using harmonic functions. A case study involving modeling of interstorm and storm durations for several Australian state capitals illustrates practical issues in calibration and identification. Because the rainfall data were stored in a binned format consisting of rainfall depths accumulated over fixed time intervals, the start and end times of storms were known only to the resolution of the fixed time interval. A likelihood function is developed which properly makes use of such information. Likelihood ratio statistics along with monthly distribution plots are used to select the number of harmonics necessary to model seasonal dependence. It is shown for Melbourne that a single harmonic adequately describes seasonal dependence, thereby reducing the number of parameters from 48 to 6.