Bayesian Estimation of A one Parameter Akshaya Distribution with Progressively Type II Censord Data

Authors

Ahlam H.Tolba, Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EgyptFollow
Ehab M. Almetwally, Department of Statistics, Faculty of Business Administration, Delta University for Science and Technology, Gamasa, 11152, Egypt\\ Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, EgyptFollow
Dina A. Ramadan, Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EgyptFollow

Abstract

A progressively type-II right censored sample has been examined in this paper for the inference about parameters for the one-parameter Akshaya distribution. As point estimates for the parameter, the maximum likelihood estimate (MLE), and Bayesian estimate are obtained. The asymptotic distribution of MLE is obtained. Also, the approximate confidence intervals (ACIs) and bootstraps confidence intervals for unknown parameter are obtained. Further, for symmetric loss functions such as squared error loss function, Bayesian estimates are obtained. Gibbs within Metropolis–Hasting samplers use the Monte Carlo chain (MCMC) technique to get the estimate of the unknown parameter from Bayes algorithm is used and the relevant credible interval (CRI) is obtained. Finally, the proposed methods are applied a real data set.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/jsap/110216

Recommended Citation

H.Tolba, Ahlam; M. Almetwally, Ehab; and A. Ramadan, Dina (2022) "Bayesian Estimation of A one Parameter Akshaya Distribution with Progressively Type II Censord Data," Journal of Statistics Applications & Probability: Vol. 11: Iss. 2, Article 16.
DOI: http://dx.doi.org/10.18576/jsap/110216
Available at: https://digitalcommons.aaru.edu.jo/jsap/vol11/iss2/16