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November, 1994 Perturbation of Normal Random Vectors by Nonnormal Translations, and an Application to HIV Latency Time Distributions
Simeon M. Berman
Ann. Appl. Probab. 4(4): 968-980 (November, 1994). DOI: 10.1214/aoap/1177004899

Abstract

Let $\mathbf{Z}$ be a normal random vector in $R^k$ and let $\mathbf{1}$ be the element of $R^k$ with equal components 1. Let $X$ be a random variable that is independent of $\mathbf{Z}$ and consider the sum $\mathbf{Z} + X\mathbf{1}$. The latter has a normal distribution in $R^k$ if and only if $X$ has a normal distribution in $R^1$. The first result of this paper is a formula for a uniform bound on the difference between the density function of $\mathbf{Z} + X\mathbf{1}$ and the density function in the case where $X$ has a suitable normal distribution. This is applied to a problem in the theory of stationary Gaussian processes which arose from the author's work on a stochastic model for the CD4 marker in the progression of HIV.

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Simeon M. Berman. "Perturbation of Normal Random Vectors by Nonnormal Translations, and an Application to HIV Latency Time Distributions." Ann. Appl. Probab. 4 (4) 968 - 980, November, 1994. https://doi.org/10.1214/aoap/1177004899

Information

Published: November, 1994
First available in Project Euclid: 19 April 2007

zbMATH: 0844.92021
MathSciNet: MR1304769
Digital Object Identifier: 10.1214/aoap/1177004899

Subjects:
Primary: 60E99
Secondary: 60G15 , 62E99 , 92A07

Keywords: Gaussian process , HIV latency time , nonnormal translation , normal random vector , posterior density

Rights: Copyright © 1994 Institute of Mathematical Statistics

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Vol.4 • No. 4 • November, 1994
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