This paper considers the use of Extreme Value Theory (EVT) to model worst-case execution times. In particular it considers the sacrifice that statistical methods make in the realism of their models in order to provide generality and precision, and if the sacrifice of realism can impact the safety of the model. The Gumbel distribution is assessed in terms of its assumption of continuous behaviou...

Abstract. We investigate properties of a version of tail comonotonicity that can be applied to absolutely continuous distributions, and give several methods for constructions of multivariate distributions with tail comonotonicity or strongest tail dependence. Archimedean copulas as mixtures of powers, and scale mixtures of a non-negative random vector with the mixing distribution having slowly ...

Recently, a novel method has been introduced to estimate the statistical significance of clustering in the direction distribution of objects. The method involves a multiscale procedure, based on the Kullback–Leibler divergence and the Gumbel statistics of extreme values, providing high discrimination power, even in presence of strong background isotropic contamination. It is shown that the meth...

Let X and Y be two nonnegative and dependent random variables following a generalized Farlie–Gumbel–Morgenstern distribution. In this short note, we study the impact of a dependence structure of X and Y on the tail behavior of XY . We quantify the impact as the limit, as x → ∞, of the quotient of Pr(XY > x) and Pr(XY ∗ > x), where X and Y ∗ are independent random variables identically distribut...

Abstract The intensity of rainfall can be considered as an essential factor in designing and operating hydraulic structures. intensity–duration–frequency (IDF) curve is used for projects such drainage networks, road culverts, bridges, many other In the field water resources engineering, IDF dependent widely on plan, designing, project. Additionally, it different flood engineering purpose this r...

The term moderate deviations is often used in the literature to mean a class of large deviation principles that, some sense, fills gap between convergence probability zero (governed by principle) and weak centered normal distribution. In this paper, examples classes kind are presented, but involved random variables converge weakly Gumbel, exponential Laplace distributions.

In this paper uniform confidence bands are constructed for nonparametric quantile estimates of regression functions. The method is based on the bootstrap, where resampling is done from a suitably estimated empirical density function (edf) for residuals. It is known that the approximation error for the uniform confidence band by the asymptotic Gumbel distribution is logarithmically slow. It is p...

We consider the maximum queue length and the maximum number of idle servers in the classical Erlang delay model and the generalization allowing customer abandonment—the M/M/n+M queue. We use strong approximations to show, under regularity conditions, that properly scaled versions of the maximum queue length and maximum number of idle servers over subintervals [0, t] in the delay models converge...

We study the optimal design of switching measurements of small Josephson junction circuits which operate in the macroscopic quantum tunnelling regime. Starting from the D-optimality criterion we derive the optimal design for the estimation of the unknown parameters of the underlying Gumbel type distribution. As a practical method for the measurements, we propose a sequential design that combine...