An Estimation of the Entropy for a Rayleigh Distribution Based on Doubly-Generalized Type-II Hybrid Censored Samples

Cho, Youngseuk; Sun, Hokeun; Lee, Kyeongjun

doi:10.3390/e16073655

Cited by 73 publications

(68 citation statements)

References 16 publications

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“…Shannon entropy is a very important inferential measure to explain the variability or uncertainty of a random variable. The Shannon entropy for a random variable X with pdf f is given by (see [24,25]),…”

Section: Estimation Of the Parameters Of Asp With The Generalized Raymentioning

confidence: 99%

Statistical Inference for Alpha-Series Process with the Generalized Rayleigh Distribution

Biçer

2019

Entropy

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In the modeling of successive arrival times with a monotone trend, the alpha-series process provides quite successful results. Both selecting the distribution of the first arrival time and making an optimal statistical inference play a crucial role in the modeling performance of the alpha-series process. In this study, when the distribution of the first arrival time is the generalized Rayleigh, the problem of statistical inference for the α , β , and λ parameters of the alpha-series process is considered. Further, in order to obtain optimal modeling performance from the mentioned alpha-series process, various estimators for the model parameters are obtained by employing different estimation methodologies such as maximum likelihood, modified maximum spacing, modified least-squares, modified moments, and modified L-moments. By a series of Monte Carlo simulations, the estimation efficiencies of the obtained estimators are evaluated through the different sample sizes. Finally, two real datasets are analyzed to illustrate the importance of modeling with the alpha-series process.

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Section: Estimation Of the Parameters Of Asp With The Generalized Raymentioning

confidence: 99%

Statistical Inference for Alpha-Series Process with the Generalized Rayleigh Distribution

Biçer

2019

Entropy

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“…We have n = 30, and we took m = 10 and R 1 = R 2 = · · · = R 10 = 2. Thus, the progressive Type II censored sample is 1,7,11,14,20,47,71,87,95,246. In this example, we take Case I (T = 70 and k = 7), Case II (T = 70 and k = 4) and Case III (T = 250 and k = 4).…”

Section: Illustrative Examplementioning

confidence: 99%

“…Abo-Eleneen [6] suggested an efficient method for the simple computation of entropy based on progressively Type II censored samples. Cho et al [7] derived estimators for the entropy function of a Rayleigh distribution based on doubly-generalized Type II hybrid censored samples by using the maximum likelihood estimator (MLE), approximate MLEs and Bayes estimators.…”

Section: Introductionmentioning

confidence: 99%

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Estimating the Entropy of a Weibull Distribution under Generalized Progressive Hybrid Censoring

Cho

Sun

Lee

2015

Entropy

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Recently, progressive hybrid censoring schemes have become quite popular in a life-testing problem and reliability analysis. However, the limitation of the progressive hybrid censoring scheme is that it cannot be applied when few failures occur before time T . Therefore, a generalized progressive hybrid censoring scheme was introduced. In this paper, the estimation of the entropy of a two-parameter Weibull distribution based on the generalized progressively censored sample has been considered. The Bayes estimators for the entropy of the Weibull distribution based on the symmetric and asymmetric loss functions, such as the squared error, linex and general entropy loss functions, are provided. The Bayes estimators cannot be obtained explicitly, and Lindley's approximation is used to obtain the Bayes estimators. Simulation experiments are performed to see the effectiveness of the different estimators. Finally, a real dataset has been analyzed for illustrative purposes.

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“…Kang et al (2012) considered the estimators of entropy of a double exponential distribution based on multiply Type II censoring. Cho et al (2014) provided the estimators of entropy of a Rayleigh distriution based on doubly-generalized Type II hybrid censoring scheme. Cho et al (2015) provided the estimators of entropy of a Weibull distribution based on generalized progressive hybrid censoring scheme.…”

Section: Introductionmentioning

confidence: 99%

Bayes estimation of entropy of exponential distribution based on multiply Type II censored competing risks data

Lee¹,

Cho

2015

Journal of the Korean Data and Information Science Society

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In lifetime data analysis, it is generally known that the lifetimes of test items may not be recorded exactly. There are also situations wherein the withdrawal of items prior to failure is prearranged in order to decrease the time or cost associated with experience. Moreover, it is generally known that more than one cause or risk factor may be present at the same time. Therefore, analysis of censored competing risks data are needed. In this article, we derive the Bayes estimators for the entropy function under the exponential distribution with an unknown scale parameter based on multiply Type II censored competing risks data. The Bayes estimators of entropy function for the exponential distribution with multiply Type II censored competing risks data under the squared error loss function (SELF), precautionary loss function (PLF) and DeGroot loss function (DLF) are provided. Lindley's approximate method is used to compute these estimators. We compare the proposed Bayes estimators in the sense of the mean squared error (MSE) for various multiply Type II censored competing risks data. Finally, a real data set has been analyzed for illustrative purposes.

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An Estimation of the Entropy for a Rayleigh Distribution Based on Doubly-Generalized Type-II Hybrid Censored Samples

Cited by 73 publications

References 16 publications

Statistical Inference for Alpha-Series Process with the Generalized Rayleigh Distribution

Statistical Inference for Alpha-Series Process with the Generalized Rayleigh Distribution

Estimating the Entropy of a Weibull Distribution under Generalized Progressive Hybrid Censoring

Bayes estimation of entropy of exponential distribution based on multiply Type II censored competing risks data

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