• Journal of the Korean Statistical Society
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• v.25 no.3
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• pp.313-336
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• 1996

In this paper we consider weak convergence of some rescaled transi-tion probabilities of a real-valued, k-th order (k $\geq$ 1) stationary Markov chain. Under the assumption that the joint distribution of K + 1 consecutive variables belongs to the domain of attraction of a multivariate extreme value distribution, the paper gives a sufficient condition for the weak convergence and characterizes the limiting distribution via the multivariate extreme value distribution.

• Journal of the Korean Statistical Society
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• v.36 no.1
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• pp.93-109
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• 2007

Gamma distributions are some of the most popular models for hydrological processes. In this paper, a very flexible family which contains the gamma distribution as a particular case is introduced. Evidence of flexibility is shown by examining the shape of its pdf and the associated hazard rate function. A comprehensive treatment of the mathematical properties is provided by deriving expressions for the nth moment, moment generating function, characteristic function, Renyi entropy and the asymptotic distribution of the extreme order statistics. Estimation and simulation issues are also considered. Finally, a detailed application to drought data from the State of Nebraska is illustrated.

• International Journal of Reliability and Applications
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• v.10 no.1
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• pp.43-57
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• 2009

In this article, we study the reliability equivalence factor of a series system. The failure rates of the system components are functions of time t. we study two cases of non-constat failure rates (i) weibull distribution (ii) linear increasing failure rate distribution. There are two methods are used to improve the given system. Two types of reliability equivalence factors are discussed. Numerical examples are presented to interpret how one can utilize the obtained results.

• International Journal of Reliability and Applications
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• v.8 no.1
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• pp.17-25
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• 2007

Maximum likelihood method is utilized to estimate the two parameters of generalized exponential distribution based on grouped and censored data. This method does not give closed form for the estimates, thus numerical procedure is used. Reliability measures for the generalized exponential distribution are calculated. Testing the goodness of fit for the exponential distribution against the generalized exponential distribution is discussed. Relevant reliability measures of the generalized exponential distributions are also evaluated. A set of real data is employed to illustrate the results given in this paper.

• Journal of the Korean Data and Information Science Society
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• v.15 no.2
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• pp.387-394
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• 2004

Zero-Inflated Poisson distribution is Poisson distribution with excess zeros. Recently defects of product hardley happen in the manufacturing process. In this case it is desirable to apply to the Zero-Inflated Poisson distribution rather than Poisson. Our target of this paper is to study the tests for changes of rate of defects after the unknown change-point. We are going to compare the powers of the two proposed tests with likelihood tests by the simulations.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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• pp.157-163
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• 2008

We study essentially disjoint one dimensionally indexed classes whose members are distribution sets of a self-similar Cantor set. The Hausdorff dimension of the union of distribution sets in a same class does not increases the Hausdorff dimension of the characteristic distribution set in the class. Further we study the Hausdorff dimension of some uncountable union of distribution sets.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1573-1581
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• 2010

we investigate the n-fold convolution of the uniform distributions. First, we are concerned with the explicit distribution function of the partial sum ${\zeta}_n$ when the random variables are independent and has identically uniform distribution, next, we determine the n-fold convolution distribution of ${\zeta}_n$ when the identically distributed condition is not satisfied.

• International Journal of Reliability and Applications
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• v.11 no.1
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• pp.23-40
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• 2010

Recently, Zaindin and Sarhan (2009) introduced a new distribution named new generalized Weibull distribution. This paper deals with the problem of estimating the parameters of this distribution in the case where the data is grouped and censored. We use both the maximum likelihood and Bayes techniques. The results obtained are illustrated on a set of real data.

• Journal of the Korean Data and Information Science Society
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• v.17 no.3
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• pp.687-705
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• 2006

In this paper we consider GPH distribution that is defined as a distribution for sum of random number of random variables following exponential distribution. We establish approximation process of general distributions to GPH distributions and offer numerical results for various cases to show the accuracy of the approximation. We also propose analysis method of delay distribution of queueing systems using approximation to GPH distributions and offer numerical results for various queueing systems to show applicability of GPH approximation.

• Journal of the Korean Statistical Society
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• v.34 no.4
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• pp.311-329
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• 2005

Skewed t distributions have attracted significant attention in the last few years. In this paper, a generalization - referred to as the skewed generalized t distribution - with the pdf f(x) = 2g(x)G(${\lambda}x$) is introduced, where g(${\cdot}$) and G (${\cdot}$) are taken, respectively, to be the pdf and the cdf of the generalized t distribution due to McDonald and Newey (1984, 1988). Several particular cases of this distribution are identified and various representations for its moments derived. An application is provided to rainfall data from Orlando, Florida.