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

Faculty Science Year: 2013
Type of Publication: Article Pages: 546-557
Authors:
Barakat, H. M, Nigm, E. M, Al-Awady, M. A
DOI: 10.1080/02331888.2011.625645
Journal: STATISTICS TAYLOR \& FRANCIS LTD Volume: 47
Research Area: Mathematics ISSN ISI:000319335000006
Keywords : weak convergence, random sample size, non-identical random vector, random maximum vector    
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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