Weak Convergence of Random Extremes from Non-identical Distributions Under General Normalization
Barakat, H., Nigm, E., El-Adil, M. (2001). Weak Convergence of Random Extremes from Non-identical Distributions Under General Normalization. EKB Journal Management System, 45(2), 182-198. doi: 10.21608/esju.2001.313814
H. M. Barakat; E. M. Nigm; M. E. El-Adil. "Weak Convergence of Random Extremes from Non-identical Distributions Under General Normalization". EKB Journal Management System, 45, 2, 2001, 182-198. doi: 10.21608/esju.2001.313814
Barakat, H., Nigm, E., El-Adil, M. (2001). 'Weak Convergence of Random Extremes from Non-identical Distributions Under General Normalization', EKB Journal Management System, 45(2), pp. 182-198. doi: 10.21608/esju.2001.313814
Barakat, H., Nigm, E., El-Adil, M. Weak Convergence of Random Extremes from Non-identical Distributions Under General Normalization. EKB Journal Management System, 2001; 45(2): 182-198. doi: 10.21608/esju.2001.313814

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  XML PDF (7.87 MB)
Document Type: Original Article
DOI: 10.21608/esju.2001.313814
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Authors
H. M. Barakat* 1; E. M. Nigm* 1; M. E. El-Adil* 2
1Dep.of Mathematics Faculty of Science, Zagazig University
2Dep.of Mathematics Faculty of Science, Helwan University
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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