## The Annals of Mathematical Statistics

### Distribution of Sum of Identically Distributed Exponentially Correlated Gamma-Variables

#### Abstract

A distribution of a sum of identically distributed Gamma-variables correlated according to an "exponential" autocorrelation law $\rho_{kj} = \rho^{|k - j|}(k, j = 1, \cdots n)$ where $\rho_{kj}$ is the correlation coefficient between the $k$th and $j$th random variables and $0 < \rho < 1$ is a given number is derived. An "approximate" distribution of the sum of these variables under the assumption that the sum itself is a Gamma-variable is given. A comparison between exact and approximate distributions for certain values of the correlation coefficient, the number of variables in the sum and the values of parameters of the initial distributions is presented.

#### Article information

Source
Ann. Math. Statist., Volume 35, Number 1 (1964), 277-283.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177703750

Digital Object Identifier
doi:10.1214/aoms/1177703750

Mathematical Reviews number (MathSciNet)
MR158459

Zentralblatt MATH identifier
0124.11205

JSTOR