A stochastic model for generating hourly hyetographs has been developed using data from observed precipitation records to simulate rainfall patterns. This model makes it possible to study maximum precipitation distributions for normal or exceptional frequencies over long periods of time. The modelling provides observations (up to 10-year frequency) of quantiles similar to those observed by directly fitting a law of statistical distribution onto an observed distribution. Differences occur for rare frequency quantiles. Modelled rainfall frequency distributions behave in an over-exponential way (i.e. greater than strictly exponential) at infinity, yielding higher results than those obtained using standard fittings. One factor that is considered in modelling can explain this behaviour: the persistence of storms within a rainfall episode which causes high rainfall accumulation. Thus modelling the observed phenomenon provides an innovative approach in studying extreme occurrences.