Let {Xi, i = 1, 2, . . .} be i.i.d. standard gaussian variables. Let Sn = X1 + . . . + Xn be the sequence of partial sums and Ln = max 0≤i<j≤n Sj − Si √ j − i . We show that the distribution of Ln, appropriately normalized, converges as n → ∞ to the Gumbel distribution. In some sense, the the random variable Ln, being the maximum of n(n+1)/2 dependent standard gaussian variables, behaves like t...

Extreme value theory has emerged as one of the most important statistical disciplines for the applied sciences. Extreme value techniques are also becoming widely used in many other disciplines. For example, for portfolio adjustment in the insurance industry; for risk assessment on financial markets; and for traffic prediction in telecommunications. Here we do some basic data analysis in extreme...

An empirically veri1ed characteristic of the expanding area of Internet is the long tailness of phenomena such as cpu time to complete a job, call holding times, 1les lengths requested, inter-arrival times and so on. Extreme values of the above quantities are liable to cause problems to the e'cient operation of the network and call for e7ective design and management. Extreme-value analysis is a...

An empirically veri1ed characteristic of the expanding area of Internet is the long tailness of phenomena such as cpu time to complete a job, call holding times, 1les lengths requested, inter-arrival times and so on. Extreme values of the above quantities are liable to cause problems to the e'cient operation of the network and call for e7ective design and management. Extreme-value analysis is a...

University of Cantabria Avenida de los Castros s/n, 39005, Santander, Spain This paper discusses the most common problems associated with the determination of design wave heights. It analyzes two common methods used In fitting wave data and shows some of the stability or inconsistency prcAlems associated with commonly used distributions. Some methods to obtain confidence intervals, detecting of...

Tropospheric ozone is one of six criteria pollutants regulated by the US EPA, and has been linked to respiratory and cardiovascular endpoints and adverse effects on vegetation and ecosystems. Regional photochemical models have been developed to study the impacts of emission reductions on ozone levels. The standard approach is to run the deterministic model under new emission levels and attribut...

This note summarizes my contributions to the estimation of extreme level curves. This problem is equivalent to estimating quantiles when covariate information is available and when their order converges to one as the sample size increases. Several estimators of these socalled ”extreme conditional quantiles” are developped and the links with boundary or frontier estimation are emphasized. 1 Extr...