The Annals of Applied Probability

Perturbation of Normal Random Vectors by Nonnormal Translations, and an Application to HIV Latency Time Distributions

Simeon M. Berman

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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.

Article information

Source
Ann. Appl. Probab., Volume 4, Number 4 (1994), 968-980.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177004899

Digital Object Identifier
doi:10.1214/aoap/1177004899

Mathematical Reviews number (MathSciNet)
MR1304769

Zentralblatt MATH identifier
0844.92021

JSTOR
links.jstor.org

Subjects
Primary: 60E99: None of the above, but in this section
Secondary: 60G15: Gaussian processes 62E99: None of the above, but in this section 92A07

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

Citation

Berman, Simeon M. Perturbation of Normal Random Vectors by Nonnormal Translations, and an Application to HIV Latency Time Distributions. Ann. Appl. Probab. 4 (1994), no. 4, 968--980. doi:10.1214/aoap/1177004899. https://projecteuclid.org/euclid.aoap/1177004899


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