Summary: D. Commenges and B. Etcheverry [Stat. Medicin 12, 1317–1324 (1993)] employed an empirical Bayes approach for obtaining a prior distribution of HIV on the basis of transmission of HIV infections from carriers to susceptibles at varying Poisson rates over time. However, the authors did not consider the double decrement pattern of HIV positive individuals, viz., the mortality of HIV positive individuals in the state of HIV and the transition of HIV infected individuals to the state of AIDS in the course of growth of HIV population. An extension of the procedure is, thus, warranted by considering the survival of HIV infected individuals and eliminating the number of AIDS cases formed during the growth of HIV populations by considering a suitable incubation period distribution. A very meaningful model of the incubation period distribution that has been derived in the paper is based on the reduction of CD-4 cells. By applying the Gauss-Aitken generalized least squares method on the linear model given by the AIDS vector and the transition matrix, the BLUE of fresh incidences over time is re-estimated.