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Article Polynomial Logistic Distribution Associated With a Cubic Polynomial(Taylor & Francis inc, 2017) Aksoy, Umit; Ostrovska, Sofiya; Ozban, Ahmet YasarLet P(x) be a polynomial monotone increasing on ( - , +). The probability distribution possessing the distribution function is called the polynomial logistic distribution with associated polynomial P. This has recently been introduced by Koutras etal., who have also demonstrated its importance for modeling financial data. In this article, the properties of the polynomial logistic distribution with an associated polynomial of degree 3 have been investigated in detail. An example of polynomial logistic distribution describing daily exchange rate fluctuations for the US dollar versus the Turkish lira is provided.Article Citation - WoS: 4Citation - Scopus: 4On the Powers of the Kummer Distribution(Academic Publication Council, 2017) Ostrovska, Sofiya; Turan, Mehmet; MathematicsThe Kummer distribution is a probability distribution, whose density is given by f (x) = cx (alpha-1)(1 + delta x)(-gamma) e(-beta x), X > 0, where alpha, beta, delta > 0, gamma is an element of R and C is a normalizing constant. In this paper, the distributions of random variable X-P, p > 0, where X has the Kummer distribution, are considered with the conditions being IFR/DFR, some properties of moments depending on the parameters and the moment-(in) determinacy. In the case of moment-indeterminacy, exemplary Stieltjes classes are constructed.Article Citation - WoS: 18Citation - Scopus: 21Failure Rates of Consecutive k-out-of-n< Systems(Springer Heidelberg, 2012) Eryilmaz, Serkan; Navarro, JorgeLinear and circular consecutive k-out-of-n systems are very popular models in reliability theory, survival analysis, and biological disciplines and other related lifetime sciences. In these theories, the failure rate function is a key notion for measuring the ageing process. In this paper we obtain some mixture representations for consecutive systems and we apply a mixture-based failure rate analysis for both linear and circular consecutive systems. In particular, we analyze the limiting behavior of the system failure rate when the time increases and we obtain some ordering properties. We first consider the popular case of systems with components having independent and identically distributed lifetimes. In practice, these assumptions may fail. So we also study the case of independent non-identically distributed component lifetimes. This case has special interest when a cold-standby redundancy is used for some components. In this sense, we analyze where to place the best components in the systems. Even more, we also study systems with dependent components by assuming that their lifetimes are exchangeable. (C) 2011 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.Article Citation - WoS: 12Citation - Scopus: 15Dynamic Reliability Evaluation of Consecutive-K System(Taylor & Francis inc, 2011) Eryilmaz, Serkan; Kan, CihangirA consecutive k-within-m-out-of-n:F system consists of n linearly ordered components and fails if and only if there are m consecutive components which include among them at least k failed components. This system model generalizes both consecutive k-out-of-n:F and k-out-of-n:F systems. In this article, we study the dynamic reliability properties of consecutive k-within-m-out-of-n:F system consisting of exchangeable dependent components. We also obtain some stochastic ordering results and use them to get simple approximation formulae for the survival function and mean time to failure of this system.
