A semiparametric generalized exponential regression model with a principled distance-based prior

The generalized exponential distribution is a well-known probability model in lifetime data analysis and several other research areas, including precipitation modeling. Despite having broad applications for independently and identically distributed observations, its uses as a generalized linear model for non-identically distributed data are limited. This paper introduces a semiparametric Bayesian generalized exponential (GE) regression model. Our proposed approach involves modeling the GE rate parameter within a generalized additive model framework. An important feature is the integration of a principled distance-based prior for the GE shape parameter; this allows the model to shrink to an exponential regression model that retains the advantages of the exponential family. We draw inferences using the Markov chain Monte Carlo algorithm and discuss some theoretical results pertaining to Bayesian asymptotics. Extensive simulations demonstrate that the proposed model outperforms simpler alternatives. The Western Ghats mountain range holds critical importance in regulating monsoon rainfall across Southern India, profoundly impacting regional agriculture. Here, we analyze daily wet-day rainfall data for the monsoon months between 1901--2022 for the Northern, Middle, and Southern Western Ghats regions. Applying the proposed model to analyze the rainfall data over 122 years provides insights into model parameters, short-term temporal patterns, and the impact of climate change. We observe a significant decreasing trend in wet-day rainfall for the Southern Western Ghats region.