Abstract.
In this paper we study the weak convergence of the generally normalized extremes (extremes under nonlinear monotone normalization) of random number of independent (nonidentically distributed) random variables. When the random sample size is assumed to converge 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 converge weakly and independent of the basic variables, the necessary and sufficient conditions for the convergence are derived.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
Acknowledgment. The authors are grateful to a referee for several helpful comments and for pointing out the extensive paper by Galambos (1992) leading to improvement of the representation of the paper.
Received January 2002
Rights and permissions
About this article
Cite this article
Barakat, H., Nigm, E. & El-Adll, M. Asymptotic properties of random extremes under general normalization from nonidentical distributions. Metrika 59, 275–287 (2004). https://doi.org/10.1007/s001840300284
Issue Date:
DOI: https://doi.org/10.1007/s001840300284