• Journal of the Korean Data and Information Science Society
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• v.7 no.1
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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

• The Korean Journal of Applied Statistics
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• v.9 no.2
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• pp.13-23
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• 1996

In this paper, we consider the Marshall and Olkin's bivariate exponential model under random censorship for the distribution of failure times of a system with two components. We propose a bootstrap testing procedure for independence and compare the powers of it with other tests via Monte Carlo simulation.

• Journal of the Korean Data and Information Science Society
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• v.10 no.1
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• pp.37-45
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• 1999

In this paper, we consider two components system having Marshall-Olkin's bivariate exponential model. For the bivariate random censorship, we obtain maximum likelihood estimators of parameters and system reliability. And we propose the methods of homogeniety and independence tests using asymptotic normality. Also we compute the estimators and p-values of the testings through Monte Carlo simulation.

• Journal of Korean Society for Quality Management
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• v.18 no.2
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• pp.101-116
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• 1990

The objectives of this thesis are : first, to estimate the parameters and Pr[X < Y] in the Marshall and Olkin's Bivariate Exponential Distribution ; and secondly, to compare the Bayes estimators of Pr[X < Y] with maximum likelihood estimator of Pr[X < Y] in the Marshall and Olkin's Bivariate Exponential Distribution. Through the Monte Carlo Simulation, we observed that the Bayes estimators of Pr[X < Y] perform better than the maximum likelihood estimator of Pr[X < Y] and the Bayes estimator of Pr[X < Y] with gamma prior distribution performs better than with vague prior distribution with respect to bias and mean squared error in the Marshall and Olkin's Bivariate Exponential Distribution.

• Journal of the Korean Data and Information Science Society
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• v.19 no.4
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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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• v.28 no.2
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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.

• Communications for Statistical Applications and Methods
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• v.3 no.3
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• pp.253-261
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• 1996

In this paper, we derive the maximum likelihood estimator of P=P(X

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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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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• v.8 no.2
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• pp.143-152
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• 1997

In this paper, we obtain maximum likelihood estimators for $P(X_{1}\;<\;X_{2})$ in the Marshall and Olkin's bivariate exponential model with bivariate censored data. The asymptotic normality of the estimator is derived. Also we propose approximate testing for $P(X_{1}\;<\;X_{2})$ based on the M.L.E. We compare the test powers under vsrious conditions through Monte Carlo simulation.

• Journal of Korean Society for Quality Management
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• v.25 no.4
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• pp.79-87
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• 1997

In this paper, we obtain maximum likelihood estimator(MLE) of a parallel system reliability for the Marshall and Olkin's bivariate exponential model with birariate type 1 consored data. The asymptotic normal distribution of the estimator is obtained. Also we construct an a, pp.oximate confidence interval for the reliability based on MLE. We present a numerical study for obtaining MLE and a, pp.oximate confidence interval of the reliability.