Geodesic
On the convergence of extreme distributions under power normalization
E. M. Nigm1
1 Department of Mathematics Faculty of Science Zagazig University Zagazig, Egypt
Applicationes Mathematicae, Tome 35 (2008) no. 2, pp. 145-153 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/am35-2-2
Keywords: paper deals convergence distribution maximum independent identically distributed random variables under power normalization measure difference between actual asymptotic distributions terms double log scale error committed replacing actual distribution maximum under power normalization its asymptotic distribution studied assuming cumulative distribution function random variables known finally examples convergence asymptotic distribution may uniform double log scale

E. M. Nigm 1

1 Department of Mathematics Faculty of Science Zagazig University Zagazig, Egypt 
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E. M. Nigm. On the convergence of extreme
 distributions under power normalization. Applicationes Mathematicae, Tome 35 (2008) no. 2, pp. 145-153. doi: 10.4064/am35-2-2

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