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2012•IEEE Transactions on CommunicationsRequires access

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

Sheetal Kalyani, R. Karthik

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Abstract

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.

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What this paper is about

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.

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Available abstract

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.

Key concepts: Gumbel distribution, Independent and identically distributed random variables, Maxima, Mathematics, Extreme value theory, Random variable, Probability density function, Context (archaeology)

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