The Tail of the Convolution of Densities and its Application to a Model of HIV-Latency Time

Let p(x) and q(x) be density functions and let (p.q)(x) be their convolution. Define w(x)=.(d/dx)logq(x)andv(x)=.(d/dx)logp(x). Under the hypothesis of the regular oscillation of the functions w and v, the asymptotic form of (p.q)(x), for x.., is obtained. The results are applied to a model previously introduced by the author for the estimation of the distribution of HIV latency time.