Bayesian analysis of an exponentiated half-logistic distribution under progressively type-II censoring

Kang, Suk Bok; Seo, Jung In; Kim, Yongku

doi:10.7465/jkdi.2013.24.6.1455

Cited by 6 publications

(8 citation statements)

References 12 publications

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“…An authentic dataset is analyzed for expository intention by employing the methods mentioned above in this section. The dataset was initially from [20] and further employed by [21,22]. The complete data set describes log times to the breakdown of an insulating fluid testing experiment and is presented in Table 2.…”

Section: Real Data Analysismentioning

confidence: 99%

Classical and Bayesian Inference of an Exponentiated Half-Logistic Distribution under Adaptive Type II Progressive Censoring

Xiong

Gui

2021

Entropy

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The point and interval estimations for the unknown parameters of an exponentiated half-logistic distribution based on adaptive type II progressive censoring are obtained in this article. At the beginning, the maximum likelihood estimators are derived. Afterward, the observed and expected Fisher’s information matrix are obtained to construct the asymptotic confidence intervals. Meanwhile, the percentile bootstrap method and the bootstrap-t method are put forward for the establishment of confidence intervals. With respect to Bayesian estimation, the Lindley method is used under three different loss functions. The importance sampling method is also applied to calculate Bayesian estimates and construct corresponding highest posterior density (HPD) credible intervals. Finally, numerous simulation studies are conducted on the basis of Markov Chain Monte Carlo (MCMC) samples to contrast the performance of the estimations, and an authentic data set is analyzed for exemplifying intention.

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Section: Real Data Analysismentioning

confidence: 99%

Classical and Bayesian Inference of an Exponentiated Half-Logistic Distribution under Adaptive Type II Progressive Censoring

Xiong

Gui

2021

Entropy

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“…where γ >0 and β >0. The prior distribution, known as the inversed gamma distribution, is used by Kang et al (2013). By combining the likelihood function (2.4) and the prior distribution (5.1), we can obtain the posterior distribution of σ.…”

Section: Bayesian Estimationmentioning

confidence: 99%

Estimation of the exponentiated half-logistic distribution based on multiply Type-I hybrid censoring

Jeon

Kang

2020

CSAM

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In this paper, we derive some estimators of the scale parameter of the exponentiated half-logistic distribution based on the multiply Type-I hybrid censoring scheme. We assume that the shape parameter λ is known. We obtain the maximum likelihood estimator of the scale parameter σ. The scale parameter is estimated by approximating the given likelihood function using two different Taylor series expansions since the likelihood equation is not explicitly solved. We also obtain Bayes estimators using prior distribution. To obtain the Bayes estimators, we use the squared error loss function and general entropy loss function (shape parameter q = −0.5, 1.0). We also derive interval estimation such as the asymptotic confidence interval, the credible interval, and the highest posterior density interval. Finally, we compare the proposed estimators in the sense of the mean squared error through Monte Carlo simulation. The average length of 95% intervals and the corresponding coverage probability are also obtained. Type-I hybrid censoring scheme isEstimation of the exponentiated half-logistic distribution based on multiply Type-I hybrid censored 49 Case I : {X 1:n < X 2:n < · · · < X r−1:n < X r:n }, if X r:n < T, Case II : {X 1:n < X 2:n < · · · < X d−1:n < X d:n < T < X d+1,n < · · · < X r:n }, if d < r, X d:n < T < X d+1:n , where r be the predetermined observation number, and T be the predetermined end time. The likelihood function is as follows.

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“…Arora et al (2010) used GHLD and derived the maximum likelihood estimate (MLE) of the shape parameter under Type-I progressive censoring with varying failure rates. Kim et al (2011) compared the MLEs and Bayes estimates of the parameter and reliability function R(t) of GHLD using progressive Type-II censoring. Seo et al (2013) obtained the MLEs and approximate MLEs of the parameters along with the approximate confidence intervals for GHLD under the hybrid censoring scheme (HCS).…”

Section: Introductionmentioning

confidence: 99%

“…(2010) used GHLD and derived the maximum likelihood estimate (MLE) of the shape parameter under Type-I progressive censoring with varying failure rates. Kim et al . (2011) compared the MLEs and Bayes estimates of the parameter and reliability function R ( t ) of GHLD using progressive Type-II censoring.…”

Section: Introductionmentioning

confidence: 99%

Estimation and prediction in generalized half logistic lifetime model using hybrid censored data

Soni

Shukla²,

Kumar

2023

IJQRM

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PurposeThis article aims to develop procedures for estimation and prediction in case of Type-I hybrid censored samples drawn from a two-parameter generalized half-logistic distribution (GHLD).Design/methodology/approachThe GHLD is a versatile model which is useful in lifetime modelling. Also, hybrid censoring is a time and cost-effective censoring scheme which is widely used in the literature. The authors derive the maximum likelihood estimates, the maximum product of spacing estimates and Bayes estimates with squared error loss function for the unknown parameters, reliability function and stress-strength reliability. The Bayesian estimation is performed under an informative prior set-up using the “importance sampling technique”. Afterwards, we discuss the Bayesian prediction problem under one and two-sample frameworks and obtain the predictive estimates and intervals with corresponding average interval lengths. Applications of the developed theory are illustrated with the help of two real data sets.FindingsThe performances of these estimates and prediction methods are examined under Type-I hybrid censoring scheme with different combinations of sample sizes and time points using Monte Carlo simulation techniques. The simulation results show that the developed estimates are quite satisfactory. Bayes estimates and predictive intervals estimate the reliability characteristics efficiently.Originality/valueThe proposed methodology may be used to estimate future observations when the available data are Type-I hybrid censored. This study would help in estimating and predicting the mission time as well as stress-strength reliability when the data are censored.

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Bayesian analysis of an exponentiated half-logistic distribution under progressively type-II censoring

Cited by 6 publications

References 12 publications

Classical and Bayesian Inference of an Exponentiated Half-Logistic Distribution under Adaptive Type II Progressive Censoring

Classical and Bayesian Inference of an Exponentiated Half-Logistic Distribution under Adaptive Type II Progressive Censoring

Estimation of the exponentiated half-logistic distribution based on multiply Type-I hybrid censoring

Estimation and prediction in generalized half logistic lifetime model using hybrid censored data

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