1,720,989 research outputs found
On Bivariate Compound Sums
No full textTank, Fatih/0000-0003-3758-396X; tank, fatih/0000-0003-3758-396X; Eryilmaz, Serkan/0000-0002-2108-1781The study of compound sums have always been very popular in the literature. Many models in insurance and engineering have been represented and solved by compound sums. In this paper, two different bivariate compound sums are proposed and studied. The phase-type distribution is applied to obtain the probability generating function of the bivariate sum. (C) 2019 Elsevier B.V. All rights reserved
Some results on the extreme distributions of surplus process with nonhomogeneous claim occurrences
Get PDFTank, Fatih/0000-0003-3758-396XIn this paper; survival (non-ruin) probability after a definite time period of an insurance company is studied in a discrete time model based on non-homogenous claim occurrences. Furthermore, distributions of the minimum and maximum levels of surplus in compound binomial risk model with non-homogeneous claim occurrences are obtained and some of its characteristics are given
On Reliability Analysis of a Two-Dependent Series System With a Standby Unit
No full texttank, fatih/0000-0003-3758-396X; Tank, Fatih/0000-0003-3758-396X; Eryilmaz, Serkan/0000-0002-2108-1781In this paper we study a series system with two active components and a single cold standby unit. The two simultaneously working components are assumed to be dependent and this dependence is modeled by a copula function. In particular, we obtain an explicit expression for the mean time to failure of the system in terms of the copula function and marginal lifetime distributions. We also provide illustrative numerical results for different copula functions and marginal lifetime distributions. (c) 2012 Elsevier Inc. All rights reserved
The Distributions of Sum, Minima and Maxima of Generalized Geometric Random Variables
No full texttank, fatih/0000-0003-3758-396X; Tank, Fatih/0000-0003-3758-396X; Eryilmaz, Serkan/0000-0002-2108-1781Geometric distribution of order as one of the generalization of well known geometric distribution is the distribution of the number of trials until the first consecutive successes in Bernoulli trials with success probability . In this paper, it is shown that this generalized distribution can be represented as a discrete phase-type distribution. Using this representation along with closure properties of phase-type distributions, the distributions of sum, minima and maxima of two independent random variables having geometric distribution of order are obtained. Numerical results are presented to illustrate the computational details
Determination of dependency parameter in joint distribution of dependent risks by fuzzy approach
No full textTank, Fatih/0000-0003-3758-396X; Gebizlioglu, Omer/0000-0002-3824-281XFrechet bounds for distribution of sum of dependent risks and Farlie-Gumbel-Morgenstein (FOM) distribution family are suggested for the analysis of dependent risks. Behaviour of the coefficient of dependency in FGM distribution is investigated by fuzzy approach. Deliberations are made for the dependency and uncertainty context. (c) 2005 Elsevier B.V. All fights reserved
Modeling of Claim Exceedances Over Random Thresholds for Related Insurance Portfolios
No full texttank, fatih/0000-0003-3758-396X; Tank, Fatih/0000-0003-3758-396X; Gebizlioglu, Ömer/0000-0002-3824-281X; Eryilmaz, Serkan/0000-0002-2108-1781Large 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.Scientific and Technological Research Council of Turkey (TUBITAK)The third author acknowledges the financial support of The Scientific and Technological Research Council of Turkey (TUBITAK) during his post doctoral research at Katholieke Universiteit Leuven, Belgium
Computing Minimal Signature of Coherent Systems Through Matrix-Geometric Distributions
No full textTank, Fatih/0000-0003-3758-396X; Eryilmaz, Serkan/0000-0002-2108-1781Signatures are useful in analyzing and evaluating coherent systems. However, their computation is a challenging problem, especially for complex coherent structures. In most cases the reliability of a binary coherent system can be linked to a tail probability associated with a properly defined waiting time random variable in a sequence of binary trials. In this paper we present a method for computing the minimal signature of a binary coherent system. Our method is based on matrix-geometric distributions. First, a proper matrix-geometric random variable corresponding to the system structure is found. Second, its probability generating function is obtained. Finally, the companion representation for the distribution of matrix-geometric distribution is used to obtain a matrix-based expression for the minimal signature of the coherent system. The results are also extended to a system with two types of components
Rekabetçi riskler taşıyan durumlar için bazı istatistiksel çıkarımlar
No full textHerhangi bir hastalığa yakalanan bireyler üzerinde yapılan klinik çalışmalarda, hastalığın izlenmesi; hastalığın ilerleyişi, tedavinin etkileri verisk faktörlerinin belirlenmesi, hastalığın seyri için önem taşımaktadır. İstatistiksel olarak bu rekabetçi risk modelleri gerçekleşmektedir. Bu tez çalışmasının amacıyeni gelişmeleri ve uygulamalarırekabetçi riskler metodolojisiyle gerçek yaşam verileriyle incelemektir. Bu bağlamda, parametrik olmayan, parametrik ve yarıparametrik çıkarım yöntemleri ile rekabetçi risk modelleri teorik olarak sayma süreci notasyonlarıyardımıyla tanıtılmıştır. Simülasyon çalışmasında üç tür başarısızlık süresi, sebebe-özel hazard fonksiyonu, alt-dağılımlıhazard fonksiyonu ve her ikisinin olduğu durumdan yararlanarak üretilmiştir. Simülasyon çalışmasına ilaveten, yarıparametrik hazard odellerin performanslarıfarklıparametre değerleri ile karşılaştırılmıştır. Son olarak, rekabetçi riskler bağlamında MEME CA tanısıkonulmuşhastalar üzerinde, hangi ölüm sebebinin üzerindedaha etkin olduğu son 10 senelik gerçek verilerle araştırılmıştır.AbstractIn clinical research which have been conducted on the people who have been contracted a disease, monitoring and progress of the diseases have crucial importance for the efficacy of the treatments, determining the riskfactors and the course of the disease. In statistics, these are achieved by competing risk models. The aim of this dissertation is to investigate the new developments and applications of the competing risks methodologies by real world data. In this regards, competing risk models are introduced theoretically by non-parametric, parametric and semi-parametric inference with counting process notation. In the simulation studies, three type failure times is generated from a cause-specific hazard function, subdistribution hazard function as well as both of them at simultaneously. In addition to the simulation studies, the performances of the semi-parametric hazard models are comparedwith different parameter values. Finally, in terms of competing risks. it is analyzed that which causes of deaths play more efficient on BREAST CA patients by real data collected for last 10 years
Doğal afetlerde sosyal zarar görebilirlik endeksi değişkenlerinin temel bileşenler analizi yöntemiyle değerlendirilmesi: 81 il bazında Türkiye uygulaması
No full textAfetler, geçmişte olduğu gibi günümüzde de toplumları tehdit etmeye devam etmektedir. Yer ve zaman gözetmeksizin meydana gelebilen afetler ciddi can, mal kayıplarına ve çevresel kayıplara sebep olmaktadır. Fakat aynı büyükteki afetlerin sebep olduğu kayıplar bölgelere ve toplumlara göre farklılık göstermektedir. Bu durumun temel nedeni, toplumların afetle başa çıkma kapasitesi ya da zarar görebilirlik seviyesinin farklılığından kaynaklanmaktadır. Türkiye’deki iller bazında bir sosyal zarar görebilirlik endeksi oluşturmak amacıyla hazırlanan bu çalışmada; 81 il bazında gelir, çalışılan iş kolları, sağlık hizmetleri, iletişim olanakları, yaşam çevresi vb. sosyal zarar görebilirliği etkileyen etmenlere ilişkin 59 değişkene ilişkin veriler derlenmiştir. Derlenen veri seti ile önce 81 il için Sosyal Zarar Görebilirlik Endeksi (SOZGE) elde edilmiştir. 59 değişkenli veri setinin temel bileşenler analizine uygunluğu incelenmiş 4 değişken diğer 4 değişkenle yüksek korelasyonlu, 5 değişken de Kaiser-Meyer-Olkin (KMO) ölçütünü sağlamadığı gerekçesiyle analizden çıkarılmıştır. 50 değişkene temel bileşenler analizi uygulanmıştır. Toplam varyansın 2/3’ünü açıklayabilen temel bileşen sayısı 4 olarak tespit edilmiştir. Belirlenen 4 temel bileşenden hareketle 81 ilin endeks değerlerine işaret eden faktör skorları elde edilmiştir. 50 değişkenin 1 temel bileşen ile temsil edilebilmesi için analiz tekrarlanmış ve elde edilen temel bileşen skorları ile 81 il bazında SOZGE değerleri elde edilmiştir. Elde edilen SOZGE değerlerine göre Şırnak ilinin sosyal zarar görebilirlik açısından 1. sırada ve Ankara ilinin sosyal zarar görebilirlik açısından 81. sırada olduğu tespit edilmiştir
Disasters continue to threaten societies today as they have in the past. Disasters that occur without regard to time and place cause serious life, property and environmental loss. But the losses caused by the same major disasters vary according to regions and societies. The underlying cause of this situation stems from the difference in the capacity or vulnerability level of societies. In this study which aims to make an index of social vulnerability; firstly, data of 59 variables considered to affect social vulnerability were collected for 81 provinces of Turkey. The Social Vulnerability Index (SOZGE) for 81 provinces was obtained by using the data of variables which are thought to affect the social vulnerability such as income, sex, education, working lines, health services, communication facilities, life environment. The suitability of 59 variable data sets to the principal components analysis (PCA) was examined and 4 variables cause of high correlation coefficient and 5 variables cause of not providing Kaiser-Meyer-Olkin (KMO) values were extracted from the analysis and the analysis of the basic components of 50 variables was applied. The number of basic components that can explain 2/3 of the total variance was determined as 4. Factor scores were obtained for 4 basic components, and index scores of 81 provinces were obtained according to these four factor scores. In order to be able to represent 50 variables with 1 principal component, the analysis was repeated and the SOZGE values were obtained for 81 provinces with the obtained basic component scores. According to SOZGE values, Şırnak provinces rank was determined as first and Ankara provinces rank was determined as 81th in terms of social vulnerability
- …
