Copulas are mathematical objects that fully capture the dependence structure among random variables and thus offer a great deal of flexibility in building multivariate stochastic models. They have widely use in, credit models, risk aggregation, portfolio selection, insurance, and reliability theory. This study will disscuss the relationship among a few copulas.
To distinguish between two or more than two models one can use the T-optimality criterion. Another criterion using for discrimination between two or more than two models is KL-criterion, which depend on the KullbackLeibler distance. KL-criterion can be used to discriminate between two non-normal models and a generalized of the KL-criterion was studied to discriminate more than two non-normal models. In this paper, more than two semiparametric models can be distinguished using generalized KL-criterion. An application was applied to illustrate the proposed technique by using three proportional hazard models via real data.
Visualizing the fatality of coronavirus is a very tricky point through the world. In this paper, a new construction via the proportional hazard rate model with Rayleigh marginal is introduced and applied on COVID‐19 data set. The statistical and reliability characteristics of bivariate Rayleigh proportional hazard (BRPH) distribution are derived. The copula dependence structure and its properties are studied. The point estimation of the marginal and dependence parameters is introduced via maximum likelihood, method of moments, and inference function for margins (IFM) method. A simulation study is carried out to examine the effectiveness and the performance of the parameter estimates. Finally, an application on COVID‐19 data is used in a comparison study between BRPH model and other constructed bivariate models. This application concerned with modeling the fatality on COVID‐19. Throughout the results of goodness‐of‐fit criteria, BRPH provides a better fit than different competitors constructed bivariate models which reflects its flexibility and applicability on modeling the fatality of COVID‐19.
In this paper, three optimality criteria will be compounded to give a new criterion, namely, CDKL-optimality for parameter estimation, estimating the area under curve and model discrimination for any kind of regression models, with homoscedastic or herteroscedastic errors, which may be Gaussian or not. CDKL-compound criterion is proposed for copula models.
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