arXiv:2611.13433v1 Announce Type: cross Abstract: The bivariate absolutely continuous exponential distribution introduced by \citet{block1974continuous} provides a model for dependent lifetimes in reliability and survival analysis. Its marginal means depend jointly and nonlinearly on the rate parameters, which complicates regression modeling and the interpretation of covariate effects on these means. In this paper, we develop two regression approaches based on a region-wise multivariate exponential-family representation. In the full-distribution approach, link functions relate the cumulant derivatives in a fixed reference region to linear predictors. These derivatives do not directly equal the marginal means, which are instead probability-weighted combinations of the regional derivatives. This relationship allows covariate effects on the marginal means to be examined. Likelihood derivatives are obtained through the chain rule, and the regression coefficients are estimated by maximum likelihood. The rate parameter estimates are then recovered through the inverse link functions and an explicit inverse mapping, with the admissible solution selected to ensure positive rates. As an alternative, we propose regression models based on the normalized conditional distribution within each region. In this setting, the cumulant derivatives coincide with the conditional means, allowing covariates to be linked directly to these means. Both approaches are evaluated through a simulation study.