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The Asymptotic Distribution of Maxima of Independent and Identically Distributed Sums of Correlated or Non-Identical Gamma Random Variables and its Applications

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2 Author(s)
Sheetal Kalyani ; Centre of Excellence in Wireless Technology, IITM Research Park, Taramani, Chennai 600113, India ; R. M. Karthik

In this paper, we show that the asymptotic probability density function (pdf) of the maxima of n independent and identically distributed (i.i.d.) sums of independent non-identically (i.n.i.d.) distributed gamma random variables (RVs) is a Gumbel pdf using Extreme Value Theory (EVT). We will also show that the asymptotic pdf of the maxima of n i.i.d. sums of correlated gamma RVs is a Gumbel pdf. Some applications in wireless communication are discussed where the maxima of n i.i.d. sums of correlated gamma RVs and maxima of n i.i.d. sums of i.n.i.d. gamma RVs arise. We discuss the utility of our results in the context of these applications.

Published in:

IEEE Transactions on Communications  (Volume:60 ,  Issue: 9 )