Elaboration of the Coale-McNeil Nuptiality Model as The Generalized Log Gamma Distribution

The Coale-McNeil nuptiality model is a particular case of the generalized log gamma distribution model. In this paper, we demonstrate that recognition of this connection allows an expansion of the possible applications of the Coale-McNeil model. As examples, we propose a procedure to develop country specific standard schedules, and illustrate the utility in regression analysis (directly and via the competing risk framework). In addition, we employ this identification to enhance the ability of the models with empirical adjustment to trace the trajectory of the lifetime schedule for cohorts which have not completed the process. We illustrate an application to Japanese female cohorts. We also propose an application to fertility projection by modeling the fertility schedule by birth order.