Papers by Ismihan Bayramoglu
Selcuk Journal of Applied Mathematics, Dec 1, 2007
In the present work, we introduce a new local dependence function characterizing dependence struc... more In the present work, we introduce a new local dependence function characterizing dependence structure between two random variables in an " neighborhood of a particular point from the domain of underlying bivariate distribution and investigate its properties. As an example the local dependence function for Farlie-Gumbel-Morgenstern distribution is provided. Also, we construct dependence maps for some pairs of random variables. We use the estimator of local dependence function to construct the dependence map. Permutation test algorithm is applied for P = 500 to obtain more accurate result in dependence map and also several examples are provided.
Reliability Engineering & System Safety, 2020
This paper considers the joint distribution of elements of a random sample and an order statistic... more This 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.
Reliability Engineering & System Safety, 1988
Reliability Engineering and System Safety is an international journal devoted to the development ... more Reliability Engineering and System Safety is an international journal devoted to the development and application of methods for the enhancement of the safety and reliability of complex technological systems, like nuclear power plants, chemical plants, hazardous waste facilities and space systems. An important aim is to achieve a balance between academic material and practical applications. The following topics are within the scope of the journal:
Distributions of exceedance statistics based on generalized order statistics are obtained for a r... more Distributions of exceedance statistics based on generalized order statistics are obtained for a random threshold model. The ordinary order statistics, progressively Type-II right censored order statistics and record values are considered as special cases. The results obtained in the article imply many results on exceedance statistics for the variety of models of ordered random variables.
Encyclopedia of Statistical Sciences, 2005
This article appeared in a journal published by Elsevier. The attached copy is furnished to the a... more This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit:
Journal of the Iranian Statistical Society, Jun 10, 2015
We consider a (n − k + 1)-out-of-n system with exchangeable lifetimes of the components. The pape... more We consider a (n − k + 1)-out-of-n system with exchangeable lifetimes of the components. The paper investigates the stochastic ordering properties of the residual lifetime of the system under condition that, at time t, at least (n − r + 1) components are alive. Some results are then extended to the case where the system has a coherent structure with exchangeable components.
Statistics, Feb 1, 2013
Let K n (a) be the number of observations in the interval (M n ,−a, M n ), where M n is the maxim... more Let K n (a) be the number of observations in the interval (M n ,−a, M n ), where M n is the maximum value in a sequence of size n. We study the asymptotic properties of K n (a) under the F α-scheme and discuss the influence of the associated sequence α n on the limit behaviour of this random variable.
In this paper two characterizations of the uniform distribution using record values will be consi... more In this paper two characterizations of the uniform distribution using record values will be considered. The first characterization is based on the relation X U (m) − X U (m−1) d = X L(m) , m > 1, where X U (m) and X L(m) denote the mth upper and lower record values, respectively. The second characterization involves the second record range.
Let X 1 , X 2 , ..., X n , ... is a sequence of independent and identically distributed (i.i.d.) ... more Let X 1 , X 2 , ..., X n , ... is a sequence of independent and identically distributed (i.i.d.) random variables (r.v.) with continuous distribution function (d.f.) F. Define a sequence of record times U (n) as follows: U (1) = 1, U (n) = min {j : j > U (n − 1), X j > X U (n−1) , n > 1. Let X U (n) be upper record values, n = 1, 2, .... Suppose that X 1 , X 2 , ..., X n , ... is an another sequence of i.i.d. r.v.-s with d.f. F. In this paper we investigate some statistics based on X U (n) , U (n) and X 1 , X 2 , ..., X n , .... A characterization of the uniform distribution is given based on X U (n) .
Journal of Computational and Applied Mathematics, Dec 1, 2018
We consider new ordereing among continous distribution functions of independent, but not necessar... more We consider new ordereing among continous distribution functions of independent, but not necessarily identically distributed random variables (INID), and introduce new order statistics defined as the observations from these ordered distribution functions. The new order statistics can be used instead of order statistics from INID random variables, and have the advantage of being independent by construction, unlike the ordinary order statistics. Some examples of ordered distribution functions and graphs are presented and some numerical examples of new order statistics are provided.
Journal of Computational and Applied Mathematics, Dec 1, 2015
ABSTRACT In this paper, we consider the mean remaining strength at the system level of two-compon... more ABSTRACT In this paper, we consider the mean remaining strength at the system level of two-component parallel and series systems in the case of possibly dependent components which are subject to a common stress. We assume that the strengths of the components have FGM, Freund’s, Marshall–Olkin and Block–Basu’s bivariate exponential models. A numerical study based on the generated data set is performed to obtain the maximum likelihood estimates of the mean remaining strength for two-component parallel system in the stress–strength setup.
Metrika, Feb 3, 2016
Two types of records in multivariate sequences are considered in this paper. According to the fir... more Two types of records in multivariate sequences are considered in this paper. According to the first definition, a multivariate observation is accepted as a record if it is not dominated in at least one of the coordinates of previous record and the first observation is a record. Some basic straightforward results concerning the distributions of record times and records according to this definition are given. The development of distribution theory for these types of record and also providing examples with available analytical results still involves challenging unsolved problems. Second, we consider records of bivariate sequences according to conditionally N-ordering, introduced in Bairamov (J Multivar Anal 97:797-809, 2006). The joint distributions of record times and distributions of record values are derived. Some examples, with particular underlying distributions demonstrating the availability of obtained formulae are provided.
Journal of Multivariate Analysis, May 1, 2011
Let Z 1 = (X 1 , Y 1), Z 2 = (X 2 , Y 2),. .. be independent and identically distributed random v... more Let Z 1 = (X 1 , Y 1), Z 2 = (X 2 , Y 2),. .. be independent and identically distributed random vectors with continuous distribution. Let L(n) and X (n) denote the nth record time and the nth record value obtained from the sequence of X s. Let Y (n) denote the concomitant of the nth record value, which relates to the sequence of Y s. We call Z i a near bivariate nth recordconcomitant observation if Z i belongs to the open rectangle (X(n) − a, X (n)) × (Y (n) − b 1 , Y (n) + b 2), where a, b 1 , b 2 > 0 and L(n) < i < L(n + 1). Asymptotic properties of the numbers of near bivariate record-concomitant observations are discussed in the present work. New techniques for generating bivariate record-concomitants, the numbers of near record observations and the numbers of near bivariate record-concomitant observations are also proposed.
Journal of Computational and Applied Mathematics, Jun 1, 2011
In life testing experiment under the setup of progressive Type II censoring we consider a new fle... more In life testing experiment under the setup of progressive Type II censoring we consider a new flexible scheme, in which the experimenter removes r * 1 (r * 1 ≤ r 1) units from the experiment if the first failure occurs before some predefined time t 1 , and removes r 1 units when the first failure occurs after time t 1. If the second failure occurs before the time t 2 , r * 2 surviving items are removed at random, otherwise r 2 surviving units are removed, (r * 2 ≤ r 2), and so on; finally, after the mth failure, all remaining items are removed. Under this setup of the experiment we study the distributions of failure times, which are entitled as flexible progressive Type II censored (FPC) order statistics. The simulation algorithm for generating FPC samples and an illustrative example for a special case of exponential distribution are also presented. Finally, a Monte Carlo study is also conducted for the expected termination time under FCP.
Statistics & Probability Letters, Feb 1, 2010
Let Z 1 = (X 1 , Y 1). .. , Z n = (X n , Y n) be independent and identically distributed random v... more Let Z 1 = (X 1 , Y 1). .. , Z n = (X n , Y n) be independent and identically distributed random vectors with continuous distribution. Let K n (a, b 1 , b 2) be the number of sample elements that belong to the open rectangle (X (n) max − a, X (n) max) × (Y (n) max − b 1 , Y (n) max + b 2)-numbers of near-maxima in the bivariate case. In the present paper, we discuss asymptotic properties of K n (a, b 1 , b 2) and K n (∞, 0, ∞).
arXiv (Cornell University), Oct 6, 2022
The concept of conditional expectation is important in applications of probability and statistics... more The concept of conditional expectation is important in applications of probability and statistics in many areas such as reliability engineering, economy, finance, and actuarial sciences due to its property of being the best predictor of a random variable as a function of another random variable. This concept also is essential in the martingale theory and theory of Markov processes. Even though, there has been studied and published many interesting properties of conditional expectations with respect to a sigmaalgebra generated by a random variable it remains an attractive subject having interesting applications in many fields. In this paper, we present some new properties of the conditional expectation of a random variable given another random variable and describe useful applications in problems of pershare-price of stock markets. The copula and dependence properties of conditional expectations as random variables are also studied. We present also some new equalities having interesting applications and results in martingale theory and Markov processes.
Communications in Statistics, Feb 1, 2005
One of the most important types of system structures is the parallel structure. In the present ar... more One of the most important types of system structures is the parallel structure. In the present article, we propose a definition for the mean residual life function of a parallel system and obtain some of its properties. The proposed definition measures the mean residual life function of a parallel system consisting of n identical and independent components under the condition that n − i, i = 0 2 n − 1, components of the system are working and other components of the system have already failed. It is shown that, for the case where the components of the system have increasing hazard rate, the mean residual life function of the system is a nonincreasing function of time. Finally, we will obtain an upper bound for the proposed mean residual life function.
Journal of Computational and Applied Mathematics, Oct 1, 2015
We consider two different sets of exchangeable samples which are assumed to be dependent. A singl... more We consider two different sets of exchangeable samples which are assumed to be dependent. A single set of observations is obtained from these two dependent samples. The distribution of single order statistic, and the joint distribution of the minimum and an arbitrary order statistic are derived. The results are illustrated in the context of reliability problem.
Communications in Statistics, Apr 23, 2014
The copula representations for conditionally independent random variables and the distribution pr... more The copula representations for conditionally independent random variables and the distribution properties of order statistics of these random variables are studied.
Journal of Applied Statistics, Mar 23, 2015
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Papers by Ismihan Bayramoglu