Bayesian Analysis of Flood Prediction Using Mixture Models of Weighted Inverse Rayleigh and Gumbel Type‐ <scp>II</scp> Distributions

ABSTRACT This article develops a two‐component mixture model combining the weighted Inverse Rayleigh (WIR) distribution and Gumbel Type‐II distribution for the estimation and prediction of flood events. The study utilizes 29 years (1990–2018) of flood data from the Federal Flood Commission (FFC) of Pakistan for the Jhelum River, using two gauging stations (Mangla and Rasul) across two catchments (U/S and D/S). Two distinct approaches, Annual Maximum series (AMS) and Peak over threshold (POT), are used for the estimation of parameters of the mixture models in a Bayesian context. Bayesian analysis is performed using the Square Error Loss Function (SELF) and Quadratic Loss Function (QLF) with gamma and beta priors. Bayes estimators and their posterior risks for both the Weighted Inverse Rayleigh and Gumbel Type‐II distributions are derived. For the Gumbel type‐II distribution, both the shape and scale parameters are treated as random. A comprehensive simulation study is conducted to examine the behavior of derived Bayes estimators and their posterior risks. The study also compares various loss functions and aims to explore a well‐fitted distribution. Additionally, it aims to determine return periods for accurate flood event predictions.