• Journal of Advanced Marine Engineering and Technology
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• 제40권2호
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• pp.131-137
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• 2016

In reliability analysis, it is quite common for the failure of any individual or item to be attributable to more than one cause. Moreover, observed data are often censored. Recently, progressive hybrid censoring schemes have become quite popular in life-testing problems and reliability analysis. However, a limitation of the progressive hybrid censoring scheme is that it cannot be applied when few failures occur before time T. Therefore, generalized progressive hybrid censoring schemes have been introduced. In this article, we derive the likelihood inference of the unknown parameters under the assumptions that the lifetime distributions of different causes are independent and exponentially distributed. We obtain the maximum likelihood estimators of the unknown parameters in exact forms. Asymptotic confidence intervals are also proposed. Bayes estimates and credible intervals of the unknown parameters are obtained under the assumption of gamma priors on the unknown parameters. Different methods are compared using Monte Carlo simulations. One real data set is analyzed for illustrative purposes.

• 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.

• Communications for Statistical Applications and Methods
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• 제31권6호
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• pp.661-675
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• 2024

The concept of length-biased distribution find various applications in biomedical area such as family history and disease, survival and intermediate events and latency period of AIDS due to blood transfusion. Also, there are many situations in biomedical analysis in which units are removed or lost from experimentation before observed. In this paper, therefore, we consider the maximum likelihood estimator (MLE) and Bayesian estimators of the unknown parameter, reliability and hazard functions of the length biased exponential distribution (LBED) under progressive hybrid censoring (PHC) scheme. We derive the Bayesian estimators of the unknown parameter, reliability and hazard functions based on flexible loss functions. Additionally, we derive the Bayesian estimators using the Lindley's approximation and Markov chain Mote Carlo (MCMC) methods. In particular, the MCMC method is used to obtain the credible interval. To compare the proposed estimators, the Monte Carlo simulation method is conducted. Finally, the leukemia patients dataset based on PHC scheme is analyzed.

• Journal of the Korean Data and Information Science Society
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• 제28권3호
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• pp.659-668
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• 2017

The inverse Weibull distribution (IWD) can be readily applied to a wide range of situations including applications in medicines, reliability and ecology. It is generally known that the lifetimes of test items may not be recorded exactly. In this paper, therefore, we consider the maximum likelihood estimation (MLE) and Bayes estimation of the entropy of a IWD under generalized progressive hybrid censoring (GPHC) scheme. It is observed that the MLE of the entropy cannot be obtained in closed form, so we have to solve two non-linear equations simultaneously. Further, the Bayes estimators for the entropy of IWD based on squared error loss function (SELF), precautionary loss function (PLF), and linex loss function (LLF) are derived. Since the Bayes estimators cannot be obtained in closed form, we derive the Bayes estimates by revoking the Tierney and Kadane approximate method. We carried out Monte Carlo simulations to compare the classical and Bayes estimators. In addition, two real data sets based on GPHC scheme have been also analysed for illustrative purposes.

• Communications for Statistical Applications and Methods
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• 제29권6호
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• pp.665-677
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• 2022

This paper proposes a new estimation method based on the maximum product of spacings for estimating unknown parameters of the three-parameter Weibull distribution under a generalized Type-II progressive hybrid censoring scheme which guarantees a constant number of observations and an appropriate experiment duration. The proposed approach is appropriate for a situation where the maximum likelihood estimation is invalid, especially, when the shape parameter is less than unity. Furthermore, it presents the enhanced performance in terms of the bias through the Monte Carlo simulation. In particular, the superiority of this approach is revealed even under the condition where the maximum likelihood estimation satisfies the classical asymptotic properties. Finally, to illustrate the practical application of the proposed approach, the real data analysis is conducted, and the superiority of the proposed method is demonstrated through a simple goodness-of-fit test.