Using the Stretched Exponential Distribution to Model Runs of Extremes in a Daily Meteorological Variable

Abstract

The stretched exponential distribution is used to create a statistical model for the frequency and duration of runs of extreme days. Extreme days are regarded here as those days when the meteorological variable concerned exceeds an upper threshold of any chosen ranking percentile or does not reach a lower threshold. This stretched exponential model represents a generalisation of a simpler modelling framework applied previously to Australian and international data. The model requires only two parameters and these parameters are location-specific and independent of the percentile of the threshold. Using the records of daily maximum and minimum temperatures in Australia and Europe, agreement between model and observations is shown to be good to very good.