On the convergence of extreme distributions under power normalization

• Autorzy: E. M. Nigm
• Języki publikacji: EN

Abstrakty

EN

This paper deals with the convergence in distribution of the maximum of n independent and identically distributed random variables under power normalization. We measure the difference between the actual and asymptotic distributions in terms of the double-log scale. The error committed when replacing the actual distribution of the maximum under power normalization by its asymptotic distribution is studied, assuming that the cumulative distribution function of the random variables is known. Finally, we show by examples that the convergence to the asymptotic distribution may not be uniform in this double-log scale.

Kategorie tematyczne

• 62G30: Order statistics; empirical distribution functions
• 62F15: Bayesian inference
• 60F05: Central limit and other weak theorems
• 62E20: Asymptotic distribution theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2008
• Tom: 35
• Numer: 2
• Strony: 145-153

Daty

wydano

2008

Twórcy

autor

E. M. Nigm

• Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt

Identyfikatory

DOI

10.4064/am35-2-2