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Öğe Cholesky Algorithm Of A Lucas Type Matrix(Ankara Univ, Fac Sci, 2024) Yılmaz, Semih; Erdoğan, BetülMany generalizations have been made for Fibonacci and Lucas number sequences and many properties have been found about these sequences. In the article [13], the authors obtained many features of these sequences with the Cholesky decomposition algorithm, using the 2 x 2 matrix belonging to a generalization of the Fibonacci sequence. In this study, it is shown that many different features can be found by using a 2 x 2 matrix belonging to the Lucas number sequence with the same method.Öğe Residual Lifetime Of System With Cold Standby Unit(2017) Tuncel, AltanIn this paper, we define and study two different residual life random variables corresponding to single unit system equipped with cold standby unit. We obtain the conditional survival functions when the lifetimes Of active and standby units are dependent. Some properties of the associated mean residual life functions are also investigated. Graphical illustrations are presented to observe time dependent behaviors of associated mean residual life functions.Öğe Complex Factorization By Chebysev Polynomials(Univ Studi Catania, Dipt Matematica, 2018) Sahin, Murat; Tan, Elif; Yilmaz, SemihLet {a(i)}, {b(i)} be real numbers for 0 <= i <= r - 1, and define a r-periodic sequence {v(n)} with initial conditions v(0) , v(1) and recurrences v(n) = a(t)v(n-1) vertical bar b(t)v(n-)(2) where n t (mod r) (n >= 2). In this paper, by aid of Chebyshev polynomials, we introduce a new method to obtain the complex factorization of the sequence {v(n)} so that we extend some recent results and solve some open problems. Also, we provide new results by obtaining the binomial sum for the sequence {v(n)} by using Chebyshev polynomials.Öğe System reliability under delta-shock model(Taylor & Francis Inc, 2018) Tuncel, Altan; Eryilmaz, Serkandelta-shock model is one of the widely studied shock models in reliability. Under this model, the system fails when the time between two consecutive shocks falls below a fixed threshold . In this paper, the survival function and the mean time to failure of the system are obtained when the times between successive shocks follow proportional hazard rate model.Öğe The eigenvalues of r-periodic tridiagonal matrices by factorization of some recursive sequences(Elsevier Science Bv, 2018) Sahin, Murat; Yilmaz, SemihWe introduce r-periodic tridiagonal matrices for given integer r >= 2. In which the entries on the principle diagonal can be any r-periodic sequence. If the entries on the principle diagonal are equal then the calculation of the eigenvalues of corresponding tridiagonal matrices is relatively easy, but when the entries are not equal, the calculation becomes much more difficult. So, some explicit formulas could be given only for the eigenvalues of certain types of the 2-periodic tridiagonal matrices so far. We give a new algorithm to find the eigenvalues of certain r-periodic tridiagonal matrices and give some results by implementing it in a symbolic programming language. Our algorithm also finds the zeros of some families of polynomials with integer coefficients. The degree of these polynomials can be chosen very high. Also, we give some new properties of the generalized continuant and then we solve an open problem by determining a complex factorization of certain r-periodic sequences. Finally, we generalize existing results by giving the explicit formulas for the eigenvalues of some r-periodic tridiagonal matrices for r = 2, 3 and 4. (C) 2017 Elsevier B.V. All rights reserved.Öğe A new wrapped exponential distribution(Springer Heidelberg, 2018) Yilmaz, Abdullah; Bicer, CenkerWe introduce a new wrapped exponential distribution named transmuted wrapped exponential (TWE) distribution, for the modeling of circular datasets by using the Transmutation Rank-Map method. This method is employed for the first time for a wrapped distribution with this study. The introduced distribution is more flexible than traditional wrapped exponential distribution. The paper provides the explicit form of important distributional properties of the introduced distribution such as expectation, median, moments, characteristic function, quantile function, hazard rate function and stress-strength reliability. Renyi and Shannon entropies are also obtained. The statistical inference problem for the TWE distribution is investigated using maximum likelihood, least squares and weighted least squares and comparative numerical study results are presented. Furthermore, we present a real dataset analysis.Öğe The Earthquake Risk Analysis Based On Copula Models For Turkey(Yildiz Technical Univ, 2017) Kizilok Kara, EmelThis study aims to explore the dependence structure between magnitude and frequency for Turkey earthquake data. In the literature, the Gutenberg Richter (GR) model based on lineer regression is often used to determine this dependence. The dependence structure is evaluated using copula models in this study. Copulas are useful statistical tool for modeling the dependence structure so it does not require assumptions such as linearity and normality. Therefore, as well as GR model, various copula functions are used to determine the magnitude-frequency relationship of earthquakes. An application is given to illustrate that the copulas can be used as alternatives to the GR model. The best copula models are selected by goodness of fit tests. Additionally, the probabilities of earthquake occurrence and the bivariate return periods are estimated for these selected copula models. It is seen that the probabilities of earthquakes occurrence for GR and copula models are almost identical, whereas the return periods based on copula models is more realistic than GR approach.Öğe The Statistical Analysis of the Earthquake Hazard for Turkey by Generalized Linear Models(Gazi Univ, 2017) Kizilok Kara, Emel; Durukan, KubraIn this paper, 4863 earthquake data of magnitude 4.0 and greater from 1900 to 2014 are statistically analyzed for the earthquake hazard in Turkey. The magnitude-frequency relationship in earthquake risk analysis is often performed by Gutenberg-Richter model. With the use of this model, information about earthquake potential of any region can be obtained by previous data and by estimating parameters such as return periods and possibilities of their occurrence. In this study, the relationship between earthquake numbers and magnitudes is modelled with the Generalized Linear Models as an alternative to Gutenberg-Richter model. Generalized Poisson Regression model and Generalized Negative Binomial Regression models as Generalized Linear Models are utilized in the study. Generalized Poisson Regression model is found as the best model when considering the dispersion parameters and model selection criteria. Exceeding probabilities and return periods are calculated for the selected years depending on yearly average occurrence number of earthquakes estimated with the Gutenberg-Richter and Generalized Poisson Regression models. According to the results, Generalized Poisson Regression model can be employed for seismic risk modelling in Turkey.Öğe Reliability and Validity of a New Test of Agility and Skill for Female Amateur Soccer Players(De Gruyter Open Ltd, 2017) Kutlu, Mehmet; Yapici, Hakan; Yilmaz, AbdullahThe aim of this study was to evaluate the Agility and Skill Test, which had been recently developed to assess agility and skill in female athletes. Following a 10 min warm-up, two trials to test the reliability and validity of the test were conducted one week apart. Measurements were collected to compare soccer players' physical performance in a 20 m sprint, a T-Drill test, the Illinois Agility Run Test, change-of-direction and acceleration, as well as agility and skill. All tests were completed following the same order. Thirty-four amateur female soccer players were recruited (age = 20.8 +/- 1.9 years; body height = 166 +/- 6.9 cm; body mass = 55.5 +/- 5.8 kg). To determine the reliability and usefulness of these tests, paired sample t-tests, intra-class correlation coefficients, typical error, coefficient of variation, and differences between the typical error and smallest worthwhile change statistics were computed. Test results showed no significant differences between the two sessions (p > 0.01). There were higher intra-class correlations between the test and retest values (r = 0.94-0.99) for all tests. Typical error values were below the smallest worthwhile change, indicating `good' usefulness for these tests. A near perfect Pearson correlation between the Agility and Skill Test (r = 0.98) was found, and there were moderate-to-large levels of correlation between the Agility and Skill Test and other measures (r = 0.37 to r = 0.56). The results of this study suggest that the Agility and Skill Test is a reliable and valid test for female soccer players and has significant value for assessing the integrative agility and skill capability of soccer players.Öğe The flexible skew Laplace distribution(Taylor & Francis Inc, 2016) Yilmaz, AbdullahSkew-symmetric distributions have been discussed by several research-ers. In this article we construct a skew-symmetric Laplace distribution, which is the generalization of distribution given by Ali etal. (2009) and Nekoukhou and Alamatsaz (2012). This new distribution contains more parameters, and this induces flexibility properties, such as unimodality or bimodality. We study on some properties of this distribution. In the last section we also provide an application with a real data. Concerning example has recently been discussed by Nekoukhou etal. (2013) to apply to their model. We compare the behavior of our distribution to their distribution on this example.Öğe Generalizing the survival signature to unrepairable homogeneous multi-state systems(Wiley, 2016) Eryilmaz, Serkan; Tuncel, AltanThe notion of signature has been widely applied for the reliability evaluation of technical systems that consist of binary components. Multi-state system modeling is also widely used for representing real life engineering systems whose components can have different performance levels. In this article, the concept of survival signature is generalized to a certain class of unrepairable homogeneous multi-state systems with multi-state components. With such a generalization, a representation for the survival function of the time spent by a system in a specific state or above is obtained. The findings of the article are illustrated for multi-state consecutive-k-out-of-n system which perform its task at three different performance levels. The generalization of the concept of survival signature to a multi-state system with multiple types of components is also presented. (C) 2016 Wiley Periodicals, Inc.Öğe Modeling Dependent Financial Assets By Dynamic Copula And Portfolio Optimization Based On Cvar(Ankara Univ, Fac Sci, 2015) Kemaloglu, Sibel Acik; Kara, Emel KizilokThis paper is concerned with the statistical modeling of the dependence structure of multivariate financial data using copula. Since financial data is greatly affected by the economic factors, it often varies according to the time. Therefore, dynamic copula model is used that takes into account the time-varying. In addition, portfolio optimization based on Mean-CVaR model is applied with Monte Carlo simulation. As an application, a portfolio with four different Indexes is constructed from the Turkish financial markets. The marginal distributions of assets in the portfolio are estimated and parameter estimates are given for the different copula models. The portfolio optimization based on CVaR is made for the portfolio created from the specified copula model.Öğe Some results on the extreme distributions of surplus process with nonhomogeneous claim occurrences(Hacettepe Univ, Fac Sci, 2015) Tank, Fatih; Tuncel, AltanIn 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.Öğe Computing the Signature of a Generalized k -Out-of-n System(Ieee-Inst Electrical Electronics Engineers Inc, 2015) Eryılmaz, Serkan; Tuncel, AltanA generalized k-out-of-n system which is denoted by ((n(1), ... , n(N)), f, k) consists N of modules ordered in a line or a circle, and the ith module is composed of n(i) components in parallel. (n(i) >= 1, i = 1, ... , N). The system fails iff there exist at least failed components or at least k consecutive failed modules. In this paper, we compute the signature of this system when n(1) = ... = n(N) = n, and present illustrative examples to demonstrate its application. Simulation based computation of the signature is provided when the modules have different numbers of components.Öğe Portfolio Optimization Of Dynamic Copula Models For Dependent Financial Data Using Change Point Approach(2016) Kara, Emel Kızılok; Kemaloğlu, Sibel AçıkIn this paper, the portfolio optimization based on CV aR is performed using the dynamic copula model for ...nancial data. Determining thebest model of dependency between ...nancial data has an important role intaking appropriate investment decisions. Due to the ...nancial data is alwaysağected by the *uctuations of the economic factors, the dynamic model washandled. On the other hand change point detection is also important for investment decisions. So this study presents an application of dynamic copulamodel with change point approach. We take the currency data (USD andEUR) from Turkish Central Bank to construct a portfolio. This study consists of two stages. In the ...rst stage, the marginal distributions and copulamodels of currency data are de...ned for full sample, and the portfolio optimization based on CV aR is performed. In the second stage, the change periodsof copula models are determined using binary segmentation method, and theportfolio optimization based on CV aR is performed for each period.Öğe Survival Probabilities For Compound Binomial Risk Model With Discrete Phase-Type Claims(2016) Tuncel, AltanDue to having useful properties in approximating to the otherdistributions and mathematically tractable, phase type distributions are commonly used in actuarial risk theory. Claim occurrence time and individualclaim size distributions are modelled by phase type distributions in literature.This paper aims to calculate the survival probabilities of an insurance company under the assumption that compound binomial risk model where theindividual claim sizes are distributed as discrete Phase Type distribution.
