optimal design for a fréchet copula marginal regression with exponential marginals

Modeling dependence using copula functions is a standard and widely used method in applied statistics‎. ‎in recent years‎, ‎experiments have been conducted in which several dependent responses are described by regression models‎, ‎and then experimental designs for these models have been carried out‎. ‎these regression models are often expressed as copula-based regression models‎, ‎so the copula parameters (if they exist) also affect the optimal design problem‎. ‎in this paper‎, ‎we consider the dependence structure of a random pair from the exponential distribution conditionally upon a covariate as a regression model‎, ‎then investigate the d-optimal design for this copula-based regression model‎. ‎the copula function that is used is the fréchet‎‎ copula‎. ‎the optimal designs obtained all have a general form depending on the selected design space.