A comprehensive decision support system for the characterization of probability distribution tails for daily precipitation

Abstract

Abstract: A conventional Decision Support System (DSS) can be used to characterize tails of probability distributions into distribution families using various graphical methods. Existing DSSs lack efficient segregation of the Lognormal distribution from the Regularly varying and Subexponential distribution families. Also, they lack the ability to identify the distributions from the hyper-exponential distributions. Recently developed graphical diagnostic tools, such as concentration profile, concentration adjusted expected shortfall, discriminant moment ratio plot, maximum-to-sum plot, and Zenga plot can classify the tails of distributions into various classes if used in an appropriate order in combination with tools of conventional DSS. The present study proposes a comprehensive DSS that alleviates the shortcomings associated with the conventional DSS and characterizes the tails of distributions into classes B\A (Pareto type), C\B (regularly varying), D\C (subexponential), E (Exponential type), hyper-exponential class (outside class E) and LN (Lognormal) distribution (the limiting case between class C and D). The robustness of the proposed DSS over the conventional DSS is established through a simulation experiment. Further, this study also evaluates the influence of the sample size on the effective implementation of the proposed DSS. Finally, the proposed DSS is applied to characterize the tails of daily gridded precipitation data over India. Results indicate that precipitation data from about 98% of grids over India exhibit distributions from heavy-tailed families. The study recommends the use of heavy-tailed distributions to model daily precipitation data over India. The study also suggests that one should rely on more than one graphical method for deducing rational conclusions regarding tail characterization.