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March, 1964 Distribution of Sum of Identically Distributed Exponentially Correlated Gamma-Variables
Samuel Kotz, John W. Adams
Ann. Math. Statist. 35(1): 277-283 (March, 1964). DOI: 10.1214/aoms/1177703750


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.


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Samuel Kotz. John W. Adams. "Distribution of Sum of Identically Distributed Exponentially Correlated Gamma-Variables." Ann. Math. Statist. 35 (1) 277 - 283, March, 1964.


Published: March, 1964
First available in Project Euclid: 27 April 2007

zbMATH: 0124.11205
MathSciNet: MR158459
Digital Object Identifier: 10.1214/aoms/1177703750

Rights: Copyright © 1964 Institute of Mathematical Statistics

Vol.35 • No. 1 • March, 1964
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