On record values and the exponent of a distribution with regularly varying upper tail-Reference-Cited by-同舟云学术

On record values and the exponent of a distribution with regularly varying upper tail

Published:1992-09 Issue:3 Volume:29 Page:575-586
ISSN:0021-9002
Container-title:Journal of Applied Probability
language:en
Short-container-title:Journal of Applied Probability

Author:

Berred Mohamed

Abstract

Let {Xn, n ≧ 1} be an i.i.d. sequence of positive random variables with a continuous distribution function having a regularly varying upper tail. Denote by {X(n), n ≧ 1} the corresponding sequence of record values. We introduce two statistics based on the sequence of successive record values and investigate their asymptotic behaviour. We also give some numerical results.

Publisher

Cambridge University Press (CUP)

Subject

Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability

Reference19 articles.

1. Almost sure convergence of the Hill estimator

2. On the almost sure behavior of sums of extreme values from a distribution in the domain of attraction of a Gumbel law;Deheuvels;Bull. Sci. Math,1990

3. Limit Theorems on Order Statistics

4. Laws of Large Numbers for Sums of Extreme Values

5. Some Results on Increments of the Wiener Process with Applications to Lag Sums of I.I.D. Random Variables

Cited by 14 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Peter Hall on Extremes: Research, teaching and supervision;Statistica Sinica;2018

2. Characterizations of Univariate Continuous Distributions;Atlantis Studies in Probability and Statistics;2017

3. Extreme Value Distributions;Atlantis Studies in Probability and Statistics;2016

4. The expected payoff to Internet auctions;Extremes;2008-11-26

5. The number of records within a random interval of the current record value;Statistical Papers;2007-01