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

• Kang, Suk Bok (2Department of Statistics, Yeungnam University) ;
• Seo, Jung In (2Department of Statistics, Yeungnam University) ;
• Kim, Yongku (Department of Statistics, Kyungpook National University)
• Accepted : 2013.08.16
• Published : 2013.11.30
• 57 32

#### Abstract

This paper develops maximum likelihood estimators (MLEs) of unknown parameters in an exponentiated half-logistic distribution based on a progressively type-II censored sample. We obtain approximate confidence intervals for the MLEs by using asymptotic variance and covariance matrices. Using importance sampling, we obtain Bayes estimators and corresponding credible intervals with the highest posterior density and Bayes predictive intervals for unknown parameters based on progressively type-II censored data from an exponentiated half logistic distribution. For illustration purposes, we examine the validity of the proposed estimation method by using real and simulated data.

#### References

1. Alaboud, F. M. (2009). Bayesian estimations for the extreme value distribution using progressive censored data and asymmetric loss. International Mathematical Forum, 8, 1603-1622.
2. Balakrishnan, N. and Kannan, N. (2001). Point and interval estimation for the logistic distribution based on progressively type-ll censored samples. In Handbook of Statistics, 20, edited by Balakrishnan, N. and Rao, C. R., Elsevier, Oxford, 431-456.
3. Balakrishnan, N., Kannan, N., Lin, C. T., and Wu, S. J. S. (2004). Inference for the extreme value distri-bution under progressively type-II censoring. Journal of Statistical Computation and Simulation, 74, 25-45. https://doi.org/10.1080/0094965031000105881
4. Balakrishnan, N. and Puthenpura, N. (1986). Best linear unbiased estimators of location and scale param-eters of the half logistic distribution. Journal of Statistics and Computer Simulation, 25, 193-204. https://doi.org/10.1080/00949658608810932
5. Balakrishnan, N. and Sandhu, R. A. (1995). A simple simulational algorithm for generating progressively type-ll censored samples. The American Statistician, 49, 229-230.
6. Balakrishnan, N. and Wong, K. H. T. (1991). Approximate MLEs for the location and scale parameters of the half-logistic distribution with type-ll right censoring. IEEE Transactions on Reliability, 40, 140-145. https://doi.org/10.1109/24.87114
7. Chen, M. H. and Shao, Q. M. (1999). Monte Carlo estimation of Bayesian credible and HPD intervals. Journal of Computational and Graphical Statistics. 8, 69-92.
8. Kang, S. B., Cho, Y. S., and Han, J. T. (2008). Estimation for the half logistic distribution under progres-sively type-ll censoring. Communications of the Korean Statistical Society, 15, 815-823. https://doi.org/10.5351/CKSS.2008.15.6.815
9. Kang, S. B., Cho, Y. S., and Han, J. T. (2009). Estimation for the half logistic distribution based on double hybrid censored samples. Communications of the Korean Statistical Society, 16, 1055-1066. https://doi.org/10.5351/CKSS.2009.16.6.1055
10. Kang, S. B. and Seo, J. I (2011). Estimation in an exponentiated half logistic distribution under progressively type-II censoring. Communications of the Korean Statistical Society, 18, 657-666. https://doi.org/10.5351/CKSS.2011.18.5.657
11. Kim, Y., Kang, S. B., and Seo, J. I. (2011). Bayesian estimations on the exponentiated distribution family with type-II right censoring. Communications of the Korean Statistical Society, 18, 603-613. https://doi.org/10.5351/CKSS.2011.18.5.603
12. Kim, Y., Kang, S. B., and Seo, J. I. (2011). Bayesian estimations on the exponentiated half triangle distri-bution under type-I hybrid censoring. Journal of the Korean Data & Information Science Society, 22, 565-574.
13. Kim, Y., Kang, S. B., and Seo, J. I. (2011). Bayesian estimation in the generalized half logistic distribution under progressively type-II censoring. Journal of the Korean Data & Information Science Society, 22, 977-987.
14. Lindley, D. V. (1980). Approximate Bayesian methods estimations. In Bayesian Statistics, edited by Bernardo, J. M., De Groot, M. H., Lindley, D. V. and Smith, A. F. M., Valencia Press, Spain.
15. Nelson, W. B. (1982). Applied life data analysis, John Willey & Sons, New York.

#### Cited by

1. Goodness-of-fit tests for the inverse Weibull or extreme value distribution based on multiply type-II censored samples vol.25, pp.4, 2014, https://doi.org/10.7465/jkdi.2014.25.4.903