On the Study of Generalized Exponential and Weibull-Type Markovian Stochastic Processes

Accepted - May 2025

Abstract

Recently, two stationary stochastic processes were introduced in Kundu (2022) and Kundu (2023), whose one-dimensional marginals follow the Generalized Exponential (GE) and Weibull distributions, respectively. In the present work, alongside discussion of these GE and Weibull processes, we propose two novel stationary Markovian processes that also have GE and Weibull distributions
as their one- dimensional marginals. We provide a detailed construction of each process. Due to non-existence of closed forms of the joint densities of the processes discussed, we use a modified method of moments based on fluctuation probabilities and sample moments to derive consistent estimators for their parameters. We also present the stochastic and distributional properties, inference procedures, simulation techniques, and real-life applications for all four processes. At the end, we provide a note on how such processes can be generalized to a more general class of Proportional Reverse Hsazard (PRH) models.