• Journal of the Korean Data and Information Science Society
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• 제7권1호
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• pp.93-104
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• 1996

In this paper, Marshall and Olkin's bivariate exponential distribution is assumed for stress and strength model. We derive the asymptotic distributions and construct some approximate confidence intervals for P(X

• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.785-804
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• 2021

The proposal of new families has been worked out by many authors over recent years. Many ways to generate new families have been developed as the methods of addition, linear combination, composition and, one of the newer, the T-X family of distributions. Using this latter method, Korkmaz et al. (2018) proposed a new class called Weibull Marshall-Olkin-G (WMO-G) family. In the present work, we propose a new distribution, based on the WMO-G family, using the Lomax distribution as baseline, called Weibull Marshall-Olkin Lomax (WMOL) distribution. The hazard rate function of this distribution can be increasing, decreasing, bathtub-shaped, decreasing-increasing-decreasing and unimodal. Some properties of the proposed model are developed. Besides that, we consider method of maximum likelihood for estimating the unknown parameters of the WMOL distribution. We provide a simulation study in order to verify the asymptotic properties of the maximum likelihood estimates. The applicability of the new distribution to modeling real life data is proved by two real data sets.

• Journal of the Korean Data and Information Science Society
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• 제19권4호
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• pp.1391-1396
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• 2008

In this paper, we consider two components system which the lifetimes have Marshall and Olkin's bivariate exponential model with bivariate type I censored data. We propose a Bayesian independent test procedure for above model using fractional Bayes factor method by O'Hagan based on improper prior distributions. And we compute the fractional Bayes factor and the posterior probabilities for the hypotheses, respectively. Also we select a hypothesis which has the largest posterior probability. Finally a numerical example is given to illustrate our Bayesian testing procedure.

• Communications for Statistical Applications and Methods
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• 제28권2호
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• pp.99-118
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• 2021

In this paper, we introduce an extended form of the inverse power Lomax model via Marshall-Olkin approach. We call it the Marshall-Olkin inverse power Lomax (MOIPL) distribution. The four- parameter MOIPL distribution is very flexible which contains some former and new models. Vital properties of the MOIPL distribution are affirmed. Maximum likelihood estimators and approximate confidence intervals are considered under Type I censored samples. Maximum likelihood estimates are evaluated according to simulation study. Bayesian estimators as well as Bayesian credible intervals under symmetric loss function are obtained via Markov chain Monte Carlo (MCMC) approach. Finally, the flexibility of the new model is analyzed by means of two real data sets. It is found that the MOIPL model provides closer fits than some other models based on the selected criteria.

• 품질경영학회지
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• 제15권1호
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• pp.20-32
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• 1987

Estimation for the parameters of a bivariate exponential (BVE) model of Marshall and Olkin (1967) is investigated for the cases of complete sampling and time-truncated parallel sampling. Maximum likelihood estimators, method of moment estimators and Bayes estimators for the parameters of a BVE model are obtained and compared with each other. A Monte Cario simulation study for a moderate sized samples indicates that the Bayes estimators of parameters perform better than their maximum likelihood and method of moment estimators.

• Communications for Statistical Applications and Methods
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• 제16권3호
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• pp.449-461
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• 2009

최근의 생산 공정은 공정의 자동화, 고객 요구의 다양화 등으로 많은 품질 특성치들을 갖는 다변량 공정의 형태가 일반적이며, 벡터 공정능력지수는 이러한 다변량 공정의 능력을 평가하기 위한 대표적인 측도라 할 수 있다. 한편 공정의 분포에 대한 정보를 정확히 파악하기 어려운 실제 현장의 상황에서 보다 정확한 공정능력을 평가할 수 있는 통계적 추정 문제는 현실적으로 중요한 문제라고 할 수 있다. 본 논문에서는 특정한 이변량 지수 공정 하에서 이변량 벡터 공정능력지수 $C_{pkl}$에 대한 신뢰영역의 추정 문제에 관하여 연구하였다. 먼저 지수분포의 특성을 고려하여 실제 현장에서 널리 사용되고 있는 가장 기본적인 일변량 공정능력지수들 중에서 규격 하한만을 고려한 형태인 $C_{pkl}$에 관하여 이변량 벡터 공정능력지수 $C_{pkl}=(C_{pklx},\;C_{pkly})$로 확장 정의하고, 이 지수의 플러그-인 추정량 및 관련 극한 확률분포를 유도하였다. 또한 이 지수에 대해 Marshall과 Olkin (1967)의 이변량 지수분포 모형을 기초로 근사 신뢰영역을 제시하였으며, 모의실험을 통하여 이변량 벡터 공정능력지수 $C_{pkl}$에 대한 95% 정규 근사(Asymptotic Normality: AN) 신뢰영역에 대한 이용가능성 및 효율성을 비교 분석하였다.