Characterization of HIV incubation distributions and some comparative studies

In this paper we use a general stochastic model to characterize the HIV incubation distributions. We generate some Monte Carlo data under different conditions and compare the fitting of HIV incubation distributions by some well known parametric models and some non-parametric methods. The parametric models include most of those that have appeared in the literature. The non-parametric methods include the Kaplan--Meier method, the EMS method, the spline approximation and the Bacchetti method. The comparison criteria are the chi-square statistic, the residual sum of squares, the AIC and the BIC. We show that the non-parametric methods, especially the EMS method, provide excellent fits in almost all cases; for the parametric models, the generalized log-logistic distributions with three and with four parameters fit better than other parametric models.