Copulas are functions that join or “couple” multivariate distributions to their one dimensional marginal distribution functions. In words, copulas are multivariate distributions whose margins are uniform on the interval (0,1). In the present article, we restrict our attention to bivariate copulas and more precisely we discuss the Ali-Mikhail-Haq bivariate model. The special case of the aforementioned model with logistic margins is studied in detail and closed formulas for its basic characteristics are derived. In addition, reliability properties for systems with two exchangeable logistic components are established.
Mathematics Subject Classification: 62E15; 62N05; 62H10; 60E05
Keywords: Bivariate copulas functions; Ali-Mikhail-Haq model; Failure rate; Mean Residual Lifetime; Parallel and Series system.