A simulation study on the correlation structure of Marshall–Olkin bivariate Weibull distribution

The correlation structure of Marshall–Olkin bivariate exponential distribution (BVE) is well known. However, we are unable to compute the correlation of Marshall–Olkin bivariate Weibull distribution analytically. Fortunately, bivariate observations from this family can be obtained easily through extensive simulations. As expected, the key factors that determine the size of the correlation are the common shape parameter α and the scale parameters λ₁λ₂ and λ₁₂ of the marginal variates. In particular, the common scale parameter λ₁₂ is found to be the most influential factor that affects the correlation. Plots from the simulations illustrate how each parameter impacts on the correlation while holding other parameters fixed. We also discuss how the correlation behaves when certain nonlinear transformations are applied to marginal variates of BVE.