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Article Citation - WoS: 11Citation - Scopus: 10Modeling of Claim Exceedances Over Random Thresholds for Related Insurance Portfolios(Elsevier, 2011) Eryilmaz, Serkan; Gebizlioglu, Omer L.; Tank, FatihLarge claims in an actuarial risk process are of special importance for the actuarial decision making about several issues like pricing of risks, determination of retention treaties and capital requirements for solvency. This paper presents a model about claim occurrences in an insurance portfolio that exceed the largest claim of another portfolio providing the same sort of insurance coverages. Two cases are taken into consideration: independent and identically distributed claims and exchangeable dependent claims in each of the portfolios. Copulas are used to model the dependence situations. Several theorems and examples are presented for the distributional properties and expected values of the critical quantities under concern. (C) 2011 Elsevier B.V. All rights reserved.Article Citation - Scopus: 1The Distribution of Wind Power from a Dispersed Array of Wind Turbine Generators and Its Reliability Based Applications(Elsevier, 2026) Eryilmaz, Serkan; Kan, Cihangir; Devrim, YilserIn this paper, the probability distribution of wind power from a dispersed array of wind turbine sites is studied considering forced outage rates of wind turbines. The wind speeds at distinct sites are assumed to be dependent and the dependence is modeled by copulas. In particular, the probability distribution of the aggregate power from two sites is exactly derived. The probability distribution of the aggregate power is also derived under the particular case when site 1 consists of n1 identical wind turbines of type 1 and site 2 consists of n2 identical wind turbines of type 2. Numerical results are presented to illustrate the theoretical findings for a chosen copula function.Article Citation - WoS: 65Citation - Scopus: 75Multivariate Copula Based Dynamic Reliability Modeling With Application To Weighted-k-out-of-n< Systems of Dependent Components(Elsevier, 2014) Eryilmaz, SerkanIn this paper, a multivariate copula based modeling methodology for dynamic reliability modeling of weighted-k-out-of-n systems is applied. The system under consideration is assumed to have n dependent components each having its own weight. It has a performance level of at least k when the total weight of operating components is k or above. Copula based expressions for the survival function and mean time to failure of such a system are obtained. Extensive numerical results are presented for Clayton and Gumbel type copulas. The behavior of survival function and mean time to failure are investigated with respect to the value of Kendall's correlation coefficient. (C) 2014 Elsevier Ltd. All rights reserved.
