A New Statistical Distribution Derived from a Clayton Copula for Modeling Bivariate Processes

Abstract Rainfall and temperature extremes have become more frequent and severe in recent times due to changing climate. Since these catastrophic occurrences directly affect a region’s hydrology, it is imperative to develop models that can project and explain the joint behavior of climate variables. Copula functions have been used relatively successfully to capture multivariate processes. With climate being a multifaceted process, there is interdependence between variables, making copula use desirable since traditional bivariate distributions do not account for the dependent structure. In this study, we introduced a bivariate exponentiated Teissier distribution based on a Clayton copula. For parameter estimation, the maximum likelihood and inference functions for margin approaches are used. A simulation study that considered various sets of parameters is also conducted in order to select the most efficient parameter estimation method. Last, the applicability of the proposed model is demonstrated using real-world data from flood and temperature processes. After fitting, the log-likelihood, Akaike information criteria (AIC), and Bayesian information criteria (BIC) values of the proposed model are −145.00, 300.00, and 311.71 for flood data, respectively, and −128.71, 267.42, and 275.98 for temperature data, respectively. Estimated parameters are for flood data and for temperature data. It is concluded that this model may be effectively used for modeling the hydrological processes for calculating the probabilities of flood and extreme temperature events.