In this paper we use a stochastic model for the HIV epidemic in homosexual populations to characterize the HIV infection and seroconversion. Using computer generated data, we compare the fitting of infection distributions and of seroconversion distributions by different parametric models as well as by nonparametric methods. The nonparametric methods include the Kaplan-Meier method, EMS method, Bacchetti's method, and the spline approximation. The parametric models include most of the models which have been used in the literature. The comparison criteria are the chi-square statistic, the AIC (Akaike Information Criterion) and the residual sums of squares. The numerical results suggest that for the proportional mixing pattern, the EMS method, the spline method, Bacchetti's method, and the generalized log-logistic distributions with three and with four parameters provide better fitting for the infection and the seroconversion distributions in most cases. For the restricted mixing patterns, the EMS method, the spline method, Bacchetti's method, and some mixtures of distributions provide close fitting to the infection and the seroconversion distributions.