Let $p(x)$ and $q(x)$ be density functions and let $(p \ast q)(x)$ be their convolution. Define $w(x) = -(d/dx)\log q(x) \text{and} v(x) = -(d/dx)\log p(x).$ Under the hypothesis of the regular oscillation of the functions $w$ and $v$, the asymptotic form of $(p \ast q)(x)$, for $x \rightarrow \infty$, is obtained. The results are applied to a model previously introduced by the author for the estimation of the distribution of HIV latency time.
Publié le : 1992-05-14
Classification:
Tail of a density function,
convolution,
regular oscillation,
regular variation,
extreme value distribution,
domain of attraction,
HIV latency time,
60E99,
60F05,
92A15
@article{1177005712,
author = {Berman, Simeon M.},
title = {The Tail of the Convolution of Densities and its Application to a Model of HIV-Latency Time},
journal = {Ann. Appl. Probab.},
volume = {2},
number = {4},
year = {1992},
pages = { 481-502},
language = {en},
url = {http://dml.mathdoc.fr/item/1177005712}
}
Berman, Simeon M. The Tail of the Convolution of Densities and its Application to a Model of HIV-Latency Time. Ann. Appl. Probab., Tome 2 (1992) no. 4, pp. 481-502. http://gdmltest.u-ga.fr/item/1177005712/