Statistical inference based on Lindley record data

Asgharzadeh, A.; Fallah, A.; Raqab, Mohammad Z.; Valiollahi, Reza

doi:10.1007/s00362-016-0788-1

Cited by 19 publications

(11 citation statements)

References 23 publications

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“…Simulation studies are conducted in Section 4 to assess the accuracy of the proposed methods and analysis of two real data sets is presented for illustrative purposes. (5) and the corresponding log-likelihood function is…”

Section: Bshmentioning

confidence: 99%

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Bayesian inference on reliability in a multicomponent stress-strength bathtub-shaped model based on record values

Pak

Khoolenjani

Rastogi

2019

Pak.j.stat.oper.res.

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In the literature, there are a well-developed estimation techniques for the reliability assessment in multicomponent stress-strength models when the information about all the experimental units are available. However, in real applications, only observations that exceed (or fall below) the current value may be recorded. In this paper, assuming that the components of the system follow bathtub-shaped distribution, we investigate Bayesian estimation of the reliability of a multicomponent stress-strength system when the available data are reported in terms of record values. Considering squared error, linex and entropy loss functions, various Bayes estimates of the reliability are derived. Because there are not closed forms for the Bayes estimates, we will use Lindleyâ€™s method to calculate the approximate Bayes estimates. Further, for comparison purposes, the maximum likelihood estimate of the reliability parameter is obtained. Finally, simulation studies are conducted in order to evaluate the performances of the proposed procedures and analysis of real data sets is provided.

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Section: Bshmentioning

confidence: 99%

“…By combining(5) with(13), the joint density function of 1  , 2  ,  and the data can be written as…”

mentioning

confidence: 99%

Bayesian inference on reliability in a multicomponent stress-strength bathtub-shaped model based on record values

Pak

Khoolenjani

Rastogi

2019

Pak.j.stat.oper.res.

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“…Since then, such ordered data has been studied extensively in the literature. The problem of making inference based on record observations from a particular distribution has received attention of many researchers, and for literature on this topic one may refer to Soliman, Abd Ellah, and Sultan (2006) for the Weibull distribution, Asgharzadeh and Fallah (2011) for the exponentiated family of distributions, Dey, Dey, Salehi, and Ahmadi (2013) for the generalized exponential distribution, Kumar, Kumar, Saran, and Jain (2017) for the Kumaraswamy-Burr III distribution, Asgharzadeh, Fallah, Raqab, and Valiollahi (2018) for the Lindley distribution, Raqab, Bdair, and Al-Aboud (2018) for the two-parameter bathtubshaped distribution, and Pak and Dey (2019) for the power Lindley distribution.…”

Section: Introductionmentioning

confidence: 99%

Estimation and Prediction for the Power-Exponential Hazard Rate Distribution Based on Record Data

Tarvirdizade

Nematollahi

2019

American Journal of Mathematical and Management Sciences

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The problems of classical and Bayesian estimation of the parameters of the power-exponential hazard rate distribution (P-EHRD) based on record values and the prediction of future record values are considered. The parameters of P-EHRD are estimated by the maximum likelihood and the least squares methods, and the Bayes estimates are obtained by the Metropolis-Hastings method under the squared error loss and LINEX loss functions. Also, an asymptotic confidence interval, two bootstrap confidence intervals and the highest posterior density (HPD) credible interval for the unknown parameters are constructed. The problem of predicting the future record values from the P-EHRD based on the past record values is considered using the maximum likelihood and Bayesian approaches. To investigate and compare the performance of the different proposed methods, a Monte Carlo simulation study is conducted. Finally, an example is presented to illustrate the estimation and prediction procedures.

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“…Recently, some work has been done on inferential procedures for the Lindley distribution based on complete and censored data [15; 16; 17; 18; 19]. Recently, Asgharzadeh et al [20] discussed the maximum likelihood and Bayesian estimation of the shape parameter of the Lindley distribution based on upper records. In this article, we consider the upper record values from the Lindley distribution.…”

Section: Introductionmentioning

confidence: 99%

On the Lindley Record Values and Associated Inference

Fallah¹,

Asgharzadeh²,

MirMostafaee³

2018

JSTA

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In this paper, we discuss the record values arising from the Lindley distribution. We compute the means, variances and covariances of the record values. These values are used to compute the best linear unbiased estimators (BLUEs) and the best linear invariant estimators (BLIEs) of the location and scale parameters. By using the BLUEs and BLIEs, we construct confidence intervals for the location and scale parameters through Monte Carlo simulations. Prediction for the future records is also discussed.

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Statistical inference based on Lindley record data

Cited by 19 publications

References 23 publications

Bayesian inference on reliability in a multicomponent stress-strength bathtub-shaped model based on record values

Bayesian inference on reliability in a multicomponent stress-strength bathtub-shaped model based on record values

Estimation and Prediction for the Power-Exponential Hazard Rate Distribution Based on Record Data

On the Lindley Record Values and Associated Inference

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