## The Annals of Mathematical Statistics

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

### 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

**Permanent link to this document**

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**

links.jstor.org

#### Citation

Kotz, Samuel; Adams, John W. Distribution of Sum of Identically Distributed Exponentially Correlated Gamma-Variables. Ann. Math. Statist. 35 (1964), no. 1, 277--283. doi:10.1214/aoms/1177703750. https://projecteuclid.org/euclid.aoms/1177703750

#### See also

- Acknowledgment of Prior Result: Samuel Kotz, John W. Adams. Acknowledgment of Priority: Distribution of Sum of Identically Distributed Exponentially Correlated Gamma-Variables. Ann. Math. Statist., Volume 35, Number 2 (1964), 925--925.Project Euclid: euclid.aoms/1177703611