WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/20.500.14365/5
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Browsing WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection by Institution Author "Bayramoglu, Ismihan (6602484525)"
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Article Citation - WoS: 2Citation - Scopus: 3Bivariate and Multivariate Distributions With Bimodal Marginals(Taylor & Francis Inc, 2020) Bayramoğlu, İsmihanWe consider simple variate distributions, which are the special cases of general elliptically contoured and Kotz type distributions. In particular, we analyze the distributions having joint probability density functions (pdf) defined as functions of allowing easy calculations of different probabilities when using transformations with spherical coordinates. In the case of we give the various examples of such pdfs whose graphs resemble a bell sunken from the middle. These distributions can be used for modelling data clustered in some areas between concentric circles or ellipses. The easy analytical form of considered distributions make it possible to use them in many applications which require simplicity of calculations. The example of probability density function allowing high correlation is also considered. We also discuss the multivariate conditional ordering of random vectors and compute the structure functions considered in the paper probability density functions. The distributions with bimodal marginals can be used in many areas, such as hydrology, biology, medicine, economics, ecology, physics, and astronomy.Article Citation - Scopus: 1Fuzzy Improved Distribution Function and Order Statistics(Elsevier, 2022) Bayramoğlu, İsmihanA new concept of fuzzy improved distribution function based on fuzzy ordering defined on the support set of a given random variable is introduced. A fuzzy improved random variable based on this distribution function is defined. The existence of such a fuzzy improved random variable follows from probability integral transformation. The order statistics based on the fuzzy ordering and fuzzy improved distribution function are considered and their distributions are studied. The need for fuzzy improved order statistics arises in reliability analysis of sensitive systems where the lifetimes of the components and the system are considered by taking into account some degree of smallness defined by membership function of a fuzzy set. Examples and graphical representations of fuzzy improved distribution functions are provided.(C) 2022 Elsevier B.V. All rights reserved.Article Citation - WoS: 2Citation - Scopus: 2Joint Distribution of a Random Sample and an Order Statistic: a New Approach With an Application in Reliability Analysis(Elsevier Sci Ltd, 2020) Bayramoğlu, İsmihanThis paper considers the joint distribution of elements of a random sample and an order statistic of the same sample. The motivation for this work stems from the important problem in reliability analysis, to estimate the number of inspections we need in order to detect failed components in a coherent system. We consider an (n - r + 1)-out-of-n system, which is intact until at least n - r + 1 of the components are alive, and it fails if the number of failed components exceeds r. The (n - r + 1)-out-of-n system is a preferred type of redundancy of fault-tolerant systems used in reliability engineering and finds wide applications in industrial and military systems. Well-known examples of this system are multiengine systems in airplane, multipump systems in hydraulic control, multicylinder engines in automobile, the radar systems, communication systems with multiple transmitters, a web host with several servers. The lifetime of the system is the rth order statistic. Assuming that some of the components failed but the system is still functioning, using the results presented in this paper it is possible to find an expected value of the number of inspections we need to do for detecting certain number of failed components.Article A Note on Fibonacci Sequences of Random Variables(University of Bologna, 2022) Bayramoglu I.; Bayramoglu, IsmihanThe aim of this paper is to introduce and investigate the new random sequence in the form {X0, X1, Xn = Xn?2 + Xn?1, n = 2, 3, ..}, referred to as Fibonacci Sequence of Random Variables (FSRV). The initial random variables X0 and X1 are assumed to be absolutely continuous with joint probability density function (pdf) fX0,X1. The FSRV is completely determined by X0 and X1 and the members of Fibonacci sequence F ? {0,1,1,2,3,5,8,13,21,34,55,89,144,...}. We examine the distributional and limit properties of the random sequence Xn,n = 0,1,2,... . © 2022 University of Bologna. All rights reserved.