SEASONAL GENERALIZED EXPONENTIAL PROBABILITY-MODELS WITH APPLICATION TO INTERSTORM AND STORM DURATIONS

A simple generalization of the exponential probability model is presen ted which provides a flexible method for identifying and fitting proba bility distributions. When coupled with likelihood-based estimation, t his approach enables a parsimonious description of seasonal dependence using harmonic functions. A case study involving modeling of intersto rm and storm durations for several Australian state capitals illustrat es practical issues in calibration and identification. Because the rai nfall data were stored in a binned format consisting of rainfall depth s accumulated over fixed time intervals, the start and end times of st orms were known only to the resolution of the fixed time interval. A l ikelihood function is developed which properly makes use of such infor mation. Likelihood ratio statistics along with monthly distribution pl ots are used to select the number of harmonics necessary to model seas onal dependence. It is shown for Melbourne that a single harmonic adeq uately describes seasonal dependence, thereby reducing the number of p arameters from 48 to 6.