This paper extends the generalized linear model framework to composite responses of the form \( Z = X + Y \) , where \( X \) and \( Y \) follow different distributions. The proposed approach enhances flexibility in modeling composite response variables arising from heterogeneous components. We study the natural exponential family associated with the composite response and show that the corresponding link and variance functions depend on a first-order nonlinear differential equation. Explicit solutions are obtained only in the Poisson–normal and exponential–normal cases. For the general case, we propose approximation and estimation methods based on Runge–Kutta approach, nonparametric techniques, and the Lagrange inversion formula. Simulation results demonstrate satisfactory performance in estimating regression coefficients. An application to insurance data illustrates the practical relevance of the proposed methodology.
