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On the convergence of extreme distributions under power normalization

E. M. Nigm — 2008

Applicationes Mathematicae

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,...

Bootstrap method for central and intermediate order statistics under power normalization

Haroon Mohamed Barakat;  E. M. Nigm;  O. M. Khaled — 2015

Kybernetika

It has been known for a long time that for bootstrapping the distribution of the extremes under the traditional linear normalization of a sample consistently, the bootstrap sample size needs to be of smaller order than the original sample size. In this paper, we show that the same is true if we use the bootstrap for estimating a central, or an intermediate quantile under power normalization. A simulation study illustrates and corroborates theoretical results.

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