• Communications for Statistical Applications and Methods
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• 제24권3호
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• pp.193-209
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• 2017

The power Lindley distribution with some of its properties is considered in this article. Maximum likelihood, least squares, maximum product spacings, and Bayes estimators are proposed to estimate all the unknown parameters of the power Lindley distribution. Lindley's approximation and Markov chain Monte Carlo techniques are utilized for Bayesian calculations since posterior distribution cannot be reduced to standard distribution. The performances of the proposed estimators are compared based on simulated samples. The waiting times of research articles to be accepted in statistical journals are fitted to the power Lindley distribution with other competing distributions. Chi-square statistic, Kolmogorov-Smirnov statistic, Akaike information criterion and Bayesian information criterion are used to access goodness-of-fit. It was found that the power Lindley distribution gives a better fit for the data than other distributions.

• Communications for Statistical Applications and Methods
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• 제28권5호
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• pp.425-445
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• 2021

A generalization of the log-logistic (LL) distribution called exponentiated log-logistic (ELL) distribution on lines of exponentiated Weibull distribution is considered. In this paper, based on progressive type-II censored samples, we have derived the maximum likelihood estimators and Bayes estimators for three parameters, the survival function and hazard function of the ELL distribution. Then, under the balanced squared error loss (BSEL) and the balanced linex loss (BLEL) functions, their corresponding Bayes estimators are obtained using Lindley's approximation (see Jung and Chung, 2018; Lindley, 1980), Tierney-Kadane approximation (see Tierney and Kadane, 1986) and Markov Chain Monte Carlo methods (see Hastings, 1970; Gelfand and Smith, 1990). Here, to check the convergence of MCMC chains, the Gelman and Rubin diagnostic (see Gelman and Rubin, 1992; Brooks and Gelman, 1997) was used. On the basis of their risks, the performances of their Bayes estimators are compared with maximum likelihood estimators in the simulation studies. In this paper, research supports the conclusion that ELL distribution is an efficient distribution to modeling data in the analysis of survival data. On top of that, Bayes estimators under various loss functions are useful for many estimation problems.

• Communications for Statistical Applications and Methods
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• 제12권3호
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• pp.729-742
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• 2005

In this paper, we discuss the propriety of the various noninformative priors for the Pareto distribution. The reference prior, Jeffreys prior and ad hoc noninformative prior which is used in several literatures will be introduced and showed that which prior gives the proper posterior distribution. The reference prior and Jeffreys prior give a proper posterior distribution, but ad hoc noninformative prior which is proportional to reciprocal of the parameters does not give a proper posterior. To compute survival function, we use the well-known approximation method proposed by Lindley (1980) and Tireney and Kadane (1986). And two methods are compared by simulation. A real data example is given to illustrate our methodology.

• Communications for Statistical Applications and Methods
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• 제25권4호
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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 Data and Information Science Society
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• 제28권5호
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• pp.1205-1215
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• 2017

In this paper, we aim to estimate two scale-parameters of exponentiated Pareto distribution (EPD) based on lower record values. Record values arise naturally in many real life applications involving data relating to weather, sport, economics and life testing studies. We calculate the Bayesian estimators for the two parameters of EPD based on lower record values. The Bayes estimators of two parameters for the EPD with lower record values under the squared error loss (SEL), linex loss (LL) and entropy loss (EL) functions are provided. Lindley's approximate method is used to compute these estimators. We compare the Bayesian estimators in the sense of the bias and root mean squared estimates (RMSE).

• Communications for Statistical Applications and Methods
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• 제27권4호
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• pp.469-486
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• 2020

Entropy is an important term in statistical mechanics that was originally defined in the second law of thermodynamics. In this paper, we consider the maximum likelihood estimation (MLE), maximum product spacings estimation (MPSE) and Bayesian estimation of the entropy of an inverse Weibull distribution (InW) under a generalized type I progressive hybrid censoring scheme (GePH). The MLE and MPSE of the entropy cannot be obtained in closed form; therefore, we propose using the Newton-Raphson algorithm to solve it. Further, the Bayesian estimators for the entropy of InW based on squared error loss function (SqL), precautionary loss function (PrL), general entropy loss function (GeL) and linex loss function (LiL) are derived. In addition, we derive the Lindley's approximate method (LiA) of the Bayesian estimates. Monte Carlo simulations are conducted to compare the results among MLE, MPSE, and Bayesian estimators. A real data set based on the GePH is also analyzed for illustrative purposes.

• 한국신뢰성학회지:신뢰성응용연구
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• 제17권3호
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• pp.213-223
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• 2017

Purpose: The purpose of this study is to arrange the life data analysis literatures based on the Bayesian method quantitatively and provide it as tables. Methods: The Bayesian method produces a more accurate estimates of other traditional methods in a small sample size, and it requires specific algorithm and prior information. Based on these three characteristics of the Bayesian method, the criteria for classifying the literature were taken into account. Results: In many studies, there are comparisons of estimation methods for the Bayesian method and maximum likelihood estimation (MLE), and sample size was greater than 10 and not more than 25. In probability distributions, a variety of distributions were found in addition to the distributions of Weibull commonly used in life data analysis, and MCMC and Lindley's Approximation were used evenly. Finally, Gamma, Uniform, Jeffrey and extension of Jeffrey distributions were evenly used as prior information. Conclusion: To verify the characteristics of the Bayesian method which are more superior to other methods in a smaller sample size, studies in less than 10 samples should be carried out. Also, comparative study is required by various distributions, thereby providing guidelines necessary.

• Communications for Statistical Applications and Methods
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• 제20권5호
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• pp.405-416
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• 2013

This paper develops a maximum profile likelihood estimator of unknown parameters of the exponentiated Gumbel distribution based on upper record values. We propose an approximate maximum profile likelihood estimator for a scale parameter. In addition, we derive Bayes estimators of unknown parameters of the exponentiated Gumbel distribution using Lindley's approximation under symmetric and asymmetric loss functions. We assess the validity of the proposed method by using real data and compare these estimators based on estimated risk through a Monte Carlo simulation.