Stochastic modeling of lightning occurrence by Nonhomogeneous Poisson Process

The characterization of lightning flash occurrence processes is key to risk analysis. Based on it, the degree of exposure of structures to direct lightning strikes can be determined, and thus, the level of protection required by the protection system can be properly set. Several studies attest that lightning flash occurrence is a natural phenomenon whose parameters vary in time and space. Looking in detail the process of occurrence leads to identification of features that allow classifying it as a member of the family of stochastic processes called counting processes. This paper offers a proposal to conceptualize the lightning flash occurrence as a Non Homogeneous Poisson type counting process, in contrast to other existing approaches which are based on the statistical concept of independent and identically distributed samples (iid) that is used in statistical inference of random variables. To justify the approach, a number of considerations is set out, including formal theoretical aspects in the field of probability and statistics, along with the analysis of the variability measure in the approach involving iid. Additionally, the paper also considers the question of statistical estimation and inference process of occurrence of lightning from the perspective of stochastic processes, offering methodological approaches that are considered useful in modeling as-Nonhomogeneous Poisson Process.