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Some Further Properties and Bayesian Inference for Inverse xgamma Distribution Under Progressive Type-II Censored Scheme

Some Further Properties and Bayesian Inference for Inverse xgamma Distribution Under Progressive... Inverse xgamma distribution is recently proposed by Yadav et al. (J Ind Prod Eng 35(1):48–55, 2018) as an inverted version of xgamma distribution. In the present article, some more statistical properties (such as, characteristic and generating functions, distributions of extreme order statistics, important entropy measures) and some additional survival and/or reliability characteristics (such as, conditional moments, mean deviation, Bonferroni and Lorenz curves, entropy, ageing intensity) of inverse xgamma distribution have been studied in detail. Classical and Bayesian inferential procedures to estimate the unknown parameter, reliability function, hazard rate function under progressively censored schemes have been investigated. Further, asymptotic confidence interval (ACI), bootstrap confidence interval (BCI) and highest posterior density (HPD) credible interval for the parameter have also been calculated. A Monte-Carlo simulation study has been performed to compare the performances of classical and Bayesian estimators of reliability function and hazard rate function. The performances of ACI, BCI and HPD credible intervals have been compared in terms of estimated average widths and coverage probabilities for the parameter. Lastly, a data set is analyzed for illustrating the proposed methodology. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Data Science Springer Journals

Some Further Properties and Bayesian Inference for Inverse xgamma Distribution Under Progressive Type-II Censored Scheme

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References (44)

Publisher
Springer Journals
Copyright
Copyright © Springer-Verlag GmbH Germany, part of Springer Nature 2020
ISSN
2198-5804
eISSN
2198-5812
DOI
10.1007/s40745-020-00286-w
Publisher site
See Article on Publisher Site

Abstract

Inverse xgamma distribution is recently proposed by Yadav et al. (J Ind Prod Eng 35(1):48–55, 2018) as an inverted version of xgamma distribution. In the present article, some more statistical properties (such as, characteristic and generating functions, distributions of extreme order statistics, important entropy measures) and some additional survival and/or reliability characteristics (such as, conditional moments, mean deviation, Bonferroni and Lorenz curves, entropy, ageing intensity) of inverse xgamma distribution have been studied in detail. Classical and Bayesian inferential procedures to estimate the unknown parameter, reliability function, hazard rate function under progressively censored schemes have been investigated. Further, asymptotic confidence interval (ACI), bootstrap confidence interval (BCI) and highest posterior density (HPD) credible interval for the parameter have also been calculated. A Monte-Carlo simulation study has been performed to compare the performances of classical and Bayesian estimators of reliability function and hazard rate function. The performances of ACI, BCI and HPD credible intervals have been compared in terms of estimated average widths and coverage probabilities for the parameter. Lastly, a data set is analyzed for illustrating the proposed methodology.

Journal

Annals of Data Science – Springer Journals

Published: Apr 1, 2023

Keywords: Bayes estimation; Maximum likelihood estimation; Progressive censoring; xgamma distribution; 62E10; 62N02; 62F15

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