On the sampling distribution of Allan factor estimator for a homogeneous Poisson process and its use to test inhomogeneities at multiple scales

► The distribution of the Allan factor for homogeneous Poisson processes is derived. ► The distribution can be used to detect inhomogeneities at multiple scales. ► The dynamics of the occurrence processes of extreme rainfall events is studied. ► The importance of analysing an appropriate range of scales is highlighted. ► Suitable surrogate data must be used as benchmarks to carry out a correct inference.