The inability to get people to regularly test and know their HIV
status has caused the widespread unavailability of correct and comprehensive
data on HIV infection especially the time at which an individual was
first infected. Hence, mathematical scientists have relied extensively on
inference obtained from small samples to estimate the HIV incubation and
seroconversion times. We set out to obtain in this paper, (i) the distribution
functions of the HIV incubation period and seroconversion time by considering
the stochastic behaviours of the members of the population under discussion,
and (ii) the method of estimation that gives the best parameter estimate by
building on previous work of Lui et al. (1988) and Medley et al. (1988).
We obtained a one-parameter family distribution for the incubation period
and a two-parameter family distribution for the seroconversion time. Data
on homosexual individuals were used since we built on past work of Lui et al. (1988). Also AIDS incidence projection was done using the backcalculation
method. However, the shortfall of the back-calculation method was
not addressed in this paper as this is meant for further research.