• Journal of the Korean Data and Information Science Society
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• v.17 no.2
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• pp.493-498
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• 2006

We shall consider the UMVUE of [P(Y>X)]$^k$ in a two parameter exponential distribution.

• Communications for Statistical Applications and Methods
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• v.18 no.1
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• pp.103-110
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• 2011

Exponential distribution is widely adopted as a lifetime model. Many authors have considered the interval estimation of the parameters of two-parameter exponential distribution based on complete and censored samples. In this paper, we consider the interval estimation of the location and scale parameters and the joint confidence region of the parameters of two-parameter exponential distribution based on upper records. A simulation study is done for the performance of all proposed confidence intervals and regions. We also propose the predictive intervals of the future records. Finally, a numerical example is given to illustrate the proposed methods.

• Journal of the Korean Data and Information Science Society
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• v.9 no.1
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• pp.71-76
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• 1998

By assuming a general progressive Type-II censored sample, we propose the minimum risk estimator (MRE) of the location parameter and the scale parameter of the two-parameter exponential distribution. An example is given to illustrate the methods of estimation discussed in this paper.

• Communications for Statistical Applications and Methods
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• v.1 no.1
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• pp.75-80
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• 1994

Parametric estimators of two parameter exponential distribution in the presence of unidentified outliers are proposed, and the means and variances of the estimators are obtained as the exact forms.

• Journal of the Korean Data and Information Science Society
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• v.19 no.4
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• pp.1409-1418
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• 2008

In this paper, we develop the reference priors for the common location parameter in two parameter exponential distributions. We derive the reference priors and prove the propriety of joint posterior distribution under the general prior including the reference priors. Through the simulation study, we show that the proposed reference prior matches the target coverage probabilities in a frequentist sense.

• Journal of the Korean Data and Information Science Society
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• v.17 no.4
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• pp.1375-1386
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• 2006

In life testing, the lifetimes of test units under the usual conditions are so long that life testing at usual conditions is impractical. Testing units are subjected to conditions of high stress to yield informations quickly. In this paper, the inferences of parameters on the three step-stress accelerated life testing are studied. The two-parameter exponential distribution with a failure rate function that a log-quadratic function of stress and the tempered failure rate model are considered. We obtain the maximum likelihood estimators of the model parameters and their confidence regions. A numerical example will be given to illustrate the proposed inferential procedures.

• Communications for Statistical Applications and Methods
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• v.25 no.4
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• pp.355-371
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• 2018

The two parameter negative exponential distribution has many practical applications in queuing theory such as the service times of agents in system, the time it takes before your next telephone call, the time until a radioactive practical decays, the distance between mutations on a DNA strand, and the extreme values of annual snowfall or rainfall; consequently, has many applications in reliability systems. This paper considers an estimation problem of stress-strength model with two parameter negative parameter exponential distribution. We introduce a maximum penalized likelihood method, Bayes estimator using Lindley approximation to estimate stress-strength model and compare the proposed estimators with regular maximum likelihood estimator for complete data. We also introduce a maximum penalized likelihood method, Bayes estimator using a Markov chain Mote Carlo technique for incomplete data. A Monte Carlo simulation study is performed to compare stress-strength model estimates. Real data is used as a practical application of the proposed model.

• Journal of the Korean Statistical Society
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• v.17 no.1
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• pp.46-55
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• 1988

Two-piece double exponential distribution (TPDE) with one piece $(X \leq 0)$ having the scale parameter $\theta_1$ while the other piece (X>0) having $\theta_2$ is considered here. Distribution of the sum of n-independent variables from such a distribution is obtained. Special cases of this distribution are also treated. Next, distribution of the ratio of two independent (TPDE) variables is derived. As an extension, distribution of $x_1/x_2x_3$ is expressed terms of hypergeometric functions. A small table gives the power of the test regarding double exponential against (TPDE).

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.923-931
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• 2005

The two parameter generalized exponential distribution was recently introduced by Gupta and Kundu (1999). It is observed that the generalized exponential distribution can be used quite effectively to analyze skewed data set. This paper develops the accelerated life test model using generalized exponential distribution and considers maximum likelihood estimation of parameters under the tampered random variable model. To show the performance of proposed maximum likelihood estimates, some simulation will be performed. Using a real data set, an example will be given.

• Journal of the Korean Data and Information Science Society
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• v.22 no.2
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• pp.361-369
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• 2011

In this paper, we develop the reference and the matching priors for the reliability function of two-parameter exponential distribution. We derive the reference priors and the matching prior, and prove the propriety of joint posterior distribution under the general prior including the reference priors and the matching prior. Through the sim-ulation study, we show that the proposed reference priors match the target coverage probabilities in a frequentist sense.