## The Annals of Applied Probability

- Ann. Appl. Probab.
- Volume 2, Number 2 (1992), 481-502.

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

#### Abstract

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.

#### Article information

**Source**

Ann. Appl. Probab., Volume 2, Number 2 (1992), 481-502.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoap/1177005712

**Digital Object Identifier**

doi:10.1214/aoap/1177005712

**Mathematical Reviews number (MathSciNet)**

MR1161063

**Zentralblatt MATH identifier**

0752.62014

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60E99: None of the above, but in this section

Secondary: 60F05: Central limit and other weak theorems 92A15

**Keywords**

Tail of a density function convolution regular oscillation regular variation extreme value distribution domain of attraction HIV latency time

#### Citation

Berman, Simeon M. The Tail of the Convolution of Densities and its Application to a Model of HIV-Latency Time. Ann. Appl. Probab. 2 (1992), no. 2, 481--502. doi:10.1214/aoap/1177005712. https://projecteuclid.org/euclid.aoap/1177005712