Bayesian Analysis of Flood Prediction Using Mixture Models of Weighted Inverse Rayleigh and Gumbel Type-II Distributions

Abstract This article develops two components mixture model of weighted inverse Rayleigh distribution (WIR) and Gumbel type-II distribution for estimation and prediction of flood event. The study uses flood data from the Federal Flood Commission of Pakistan (FFC) over 29 years (1990–2018) of the Jhelum River using two gauging stations, Mangla and Rasul, for two catchments (upstream, downstream) each. Two distinct approaches Annual Maximum series (AMS) and Peak over threshold (POT) are used for estimation of parameters of said mixture models in Bayesian context. Bayesian analysis is performed using Square Error Loss Function (SELF) and Quadratic Loss Function (QLF) with gamma and beta informative priors. Bayes estimators and their posterior risks for Weighted Inverse Rayleigh distribution and Gumble-type-II distribution are derived. For the case of Gumbel type-II, both the shape and scale parameters are considered random. A comprehensive study is conducted to thoroughly examine the behavior of derived Bayes estimators and their posterior risks. The study involves comparing various loss functions and aims to explore well-fitted distribution. Additionally, it seeks to determine return periods in order to predict future flood events accurately.