Weak Convergence of Random Extremes from Non-identical Distributions Under General Normalization | ||||
The Egyptian Statistical Journal | ||||
Article 6, Volume 45, Issue 2, December 2001, Page 182-198 | ||||
Document Type: Original Article | ||||
DOI: 10.21608/esju.2001.313814 | ||||
View on SCiNiTO | ||||
Abstract | ||||
In this paper we study the weak convergence of the generally normalized extremes (extremes under nonlinear monotone normalization) of random number of independent (non-identically) random variables. When the random sample size is assumed to be converged in probability and the interrelation between the basic variables and their random size is not restricted, the limit forms as well as the sufficient conditions of convergence are derived. Moreover, when the random sample size is assumed to be converged weakly and independent of the basic variables, the necessary and sufficient conditions for the convergence are derived. | ||||
Keywords | ||||
Weak Convergence; Extremes - General Nonlinear Normalization - Random Sample Size | ||||
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