Scholarly Output Search Results

Now showing 1 - 3 of 3

Citation - WoS: 27
Citation - Scopus: 30
The Distributions of Sum, Minima and Maxima of Generalized Geometric Random Variables
(Springer, 2015) Tank, Fatih; Eryilmaz, Serkan
Geometric 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.
Citation - WoS: 11
Citation - Scopus: 10
Modeling of Claim Exceedances Over Random Thresholds for Related Insurance Portfolios
(Elsevier, 2011) Eryilmaz, Serkan; Gebizlioglu, Omer L.; Tank, Fatih
Large 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.
Citation - WoS: 21
Citation - Scopus: 29
On Reliability Analysis of a Two-Dependent Series System With a Standby Unit
(Elsevier Science inc, 2012) Eryilmaz, Serkan; Tank, Fatih
In 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.

Journal	Count
Journal of Computational and Applied Mathematics	2
Insurance: Mathematics and Economics	1
Japanese Journal of Statistics and Data Science	1
Applied Mathematics and Computation	1
Statistical Papers	1

Tank, Fatih

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Sustainable Development Goals

NO POVERTY

ZERO HUNGER

GOOD HEALTH AND WELL-BEING

QUALITY EDUCATION

GENDER EQUALITY

CLEAN WATER AND SANITATION

AFFORDABLE AND CLEAN ENERGY

DECENT WORK AND ECONOMIC GROWTH

INDUSTRY, INNOVATION AND INFRASTRUCTURE

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SUSTAINABLE CITIES AND COMMUNITIES

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PEACE, JUSTICE AND STRONG INSTITUTIONS

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23

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173

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7

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22

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136

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8

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7

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37/0

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0

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0

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72

Scopus Citation Count

88

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0

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9.00

Scopus Citations per Publication

11.00

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1

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