Proceedings of the Japan Academy, Series A, Mathematical Sciences

A note on random permutations and extreme value distributions

Pavle Mladenovi\'{c}

Full-text: Open access

Abstract

Let $\Omega_n$ be the set of all permutations of the set $N_n = \{1, 2, \dots, n\}$ and let us suppose that each permutation $\omega = (a_1, \dots, a_n) \in \Omega_n$ has probability $1/n!$. For $\omega = (a_1, \dots, a_n)$ let $X_{nj} = |a_j - a_{j+1}|$, $j \in N_n$, $a_{n+1} = a_1$, $M_n = \max\{X_{n1}, \dots, X_{nn}\}$. We prove herein that the random variable $M_n$ has asymptotically the Weibull distribution, and give some remarks on the domains of attraction of the Fréchet and Weibull extreme value distributions.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 78, Number 8 (2002), 157-160.

Dates
First available in Project Euclid: 23 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.pja/1148392611

Digital Object Identifier
doi:10.3792/pjaa.78.157

Mathematical Reviews number (MathSciNet)
MR1935573

Zentralblatt MATH identifier
1019.60050

Subjects
Primary: 60G70: Extreme value theory; extremal processes
Secondary: 05A05: Permutations, words, matrices

Keywords
Random permutations maximum of random sequence Leadbetter's mixing condition extreme value distributions domains of attraction

Citation

Mladenovi\'{c}, Pavle. A note on random permutations and extreme value distributions. Proc. Japan Acad. Ser. A Math. Sci. 78 (2002), no. 8, 157--160. doi:10.3792/pjaa.78.157. https://projecteuclid.org/euclid.pja/1148392611


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