The Annals of Applied Probability

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

Simeon M. Berman

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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


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