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Limit theorems for random maximum of independent and non-identically distributed random vectors

H. M. Barakat, El-Sayed M. Nigm, Metwally Alsayed Alawady

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Abstract

In this paper, we study the weak convergence of the random maximum of independent and non-identical random vectors. When the random sample size is assumed to be independent of the basic variables and its distribution function is assumed to converge weakly to a non-degenerate limit, the necessary and sufficient conditions for the weak convergence of the random maximum are derived. An illustrative example is given.

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What this paper is about

In this paper, we study the weak convergence of the random maximum of independent and non-identical random vectors. When the random sample size is assumed to be independent of the basic variables and its distribution function is assumed to converge weakly to a non-degenerate limit, the necessary and sufficient conditions for the weak convergence of the random maximum are derived. An illustrative example is given.

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Available abstract

In this paper, we study the weak convergence of the random maximum of independent and non-identical random vectors. When the random sample size is assumed to be independent of the basic variables and its distribution function is assumed to converge weakly to a non-degenerate limit, the necessary and sufficient conditions for the weak convergence of the random maximum are derived. An illustrative example is given.

Key concepts: Mathematics, Independent and identically distributed random variables, Convergence of random variables, Weak convergence, Random variable, Multivariate random variable, Limit (mathematics), Sum of normally distributed random variables

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