New estimators based on the likelihood depth for the examples of 2-dimensional, one-parametric Gumbel-Copula (and 2-dimensional Gauss-distribution) and in a second step for the Weibulldistribution are presented. The copula model has a variety of applications because it models dependence structures, e.g. in finance, in the analysis of credit risks. Copulas can also be used in the simulation of t...

Zusammenfassung Emil J. Gumbel ist der Namensgeber jährlichen Gumbel-Vorlesung auf Statistischen Woche. Leider dieser Vorlesung nur noch wenigen Teilnehmern und Vortragenden bekannt. Dieser Artikel möchten diesem Defizit abhelfen. Denn war nicht irgendeiner statistischen Verteilung. Der Aufsatz beschreibt den Lebensweg Gumbels vom Weltkriegsteilnehmer zu einem weithin bekannten Pazifisten, die ...

We study a stochastic model of infection spreading on a network. At each time step a node is chosen at random, along with one of its neighbors. If the node is infected and the neighbor is susceptible, the neighbor becomes infected. How many time steps T does it take to completely infect a network of N nodes, starting from a single infected node? An analogy to the classic "coupon collector" prob...

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Abstract This paper deals with the availability analysis of a complex system that consists of two subsystems namely subsystem 1 and subsystem 2.Subsystem 1 is working under k-out of –n good policy and subsystem 2 has two identical units in parallel configuration. Controller for proper functioning controls the subsystems 1. All failure rates are constant and follow exponential distribution but r...

Best practice life expectancy has recently been modeled using extreme value theory. In this paper we present the Gumbel autoregressive model of order one—Gumbel AR(1)—as an option for modeling best expectancy. This class represents a neat and coherent framework time series extremes. The distribution accounts nature expectancy, while AR structure temporal dependence in series. Model diagnostics ...

Inconsistency of decision maker’s preferences may be measured as a number of violation of a transitivity rule or by some other measure like consistency index in Analytical Hierarchy Process. In Potential Method, inconsistency is measured by an angle between the preference flow and the column space of the incidence matrix. In this article, a random study is performed to determine the upper bound...

We study the rescaled probability distribution of the critical depinning force of an elastic system in a random medium. We put in evidence the underlying connection between the critical properties of the depinning transition and the extreme value statistics of correlated variables. The distribution is Gaussian for all periodic systems, while in the case of random manifolds there exists a family...