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May, 1992 The Tail of the Convolution of Densities and its Application to a Model of HIV-Latency Time
Simeon M. Berman
Ann. Appl. Probab. 2(2): 481-502 (May, 1992). DOI: 10.1214/aoap/1177005712

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.

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Simeon M. Berman. "The Tail of the Convolution of Densities and its Application to a Model of HIV-Latency Time." Ann. Appl. Probab. 2 (2) 481 - 502, May, 1992. https://doi.org/10.1214/aoap/1177005712

Information

Published: May, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0752.62014
MathSciNet: MR1161063
Digital Object Identifier: 10.1214/aoap/1177005712

Subjects:
Primary: 60E99
Secondary: 60F05 , 92A15

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

Rights: Copyright © 1992 Institute of Mathematical Statistics

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