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In this study, we use the idea of the hierarchical model (HM) to estimate an unknown parameter of the hierarchical Poisson-Gamma model using the E-Bayesian (E-B) theory. We propose the idea of hierarchical probability function instead of the traditional hierarchical prior density function. We aim to infer E-B estimates with respect to the conjugate Gamma prior distribution along with the E-posterior risks on the basis of different symmetric and asymmetric loss functions (LFs) under restricted and unrestricted parameter spaces using uniform hyperprior. Whereas, E-B estimators are compared with maximum likelihood estimators (MLEs) using mean squared error (MSE). Monte Carlo simulations are prosecuted to study the efficiency of E-B estimators empirically. It is shown that the LFs under a restricted parameter space dominate to estimate the parameter of the hierarchical Poisson-Gamma model. It is also found that the E-B estimators are more precise than MLEs, and Stein’s LF has the least E-PR. Moreover, the application of outcomes to a real-life example has been made for analysis, comparison, and motivation.

Drought is one of the most multifaceted hydrologic phenomena, affecting several factors such as soil moisture, surface runoff, and significant water shortages. Therefore, monitoring and assessing drought occurrences based on a single drought index are inadequate. The current study develops a multiscalar weighted amalgamated drought index (MWADI) to amalgamate multiple drought indices. The MWADI is mainly based on the normalized average dependence posterior probabilities (ADPPs). These ADPPs are obtained from Bayesian networks (BNs)-based Markov Chain Monte Carlo (MCMC) simulations. Results have shown that the MWADI correlates more with the standardized precipitation index (SPI) and the standardized precipitation temperature index (SPTI). As proposed, the MWADI synthesizes drought characteristics of different multiscalar drought indices to reduce the uncertainty of individual drought indices and provide a comprehensive drought assessment.