Research Projects

In many practical scenarios, including finance, insurance, environmental sciences, hydrology, system reliability, etc., it is often of interest to study the various notions of dependence among the observed variables. The understanding of dependencies among variables is often centered on two fundamental questions (a) what is the structure of dependence; and (b) how strong is the dependence among the variables? In this regard, copulas provide a powerful approach by separating marginal distributions from the dependence structure, enabling the modeling of complex dependencies between random variables. The main aims of this project are the following: (a) to develop a flexible bivariate copula, by overcoming the longstanding limitation for modeling negative dependent data, that can take value in the whole unit square with the correlation coefficient having a negative value in the full range and satisfy all the popular notions of negative dependence such as negative quadrant dependent, left tail increasing, right tail decreasing, negative likelihood ratio-dependent, stochastically decreasing; (b) to develop nonparametric estimators for copula satisfying different dependence property such as left tail decreasing, right tail increasing, stochastic increasing, stochastic decreasing, likelihood ratio-dependent, and expectation dependence separately which will remain a valid copula for any sample size and propose methodologies to test for such properties of an unknown copula.