Abstract
In this paper, we consider the estimation of R = Pr(X > Y ) based on lower record values
when X and Y are independently but not identically exponentiated Gumbel distributed random variables.
The maximum likelihood, Bayes and empirical Bayes estimators of R are obtained and their properties are
studied. Confidence intervals, exact and approximate, as well as the Bayesian credible sets for R are obtained.
A simulation study is conducted to investigate and compare the performance of the intervals.
Keywords
Bayes estimation empirical Bayes estimation exponentiated Gumbel distribution maximum likelihood estimation record values stress-strength reliability
References
- Abdi, M. (2014). Confidence interval for the two-parameter exponentiated Gumbel distribution based on record values. International Journal of Applied Operational Research, 4, 73–80.
- Ahsanullah, M. (2004). Record Values. University Press of America Inc., Lanham, Maryland, USA : Theory and Applications.
- Arnold, B. C., Balakrishnan, N., and Nagaraja, H.N. (1998). Records. Wiley.
- Chen, Ming-Hui., Shao, Qi-Man. (1999). Monte Carlo estimation of Bayesian credible and HPD intervals. Journal of Computational and Graphical Statistics, 8, 69–92.
- DiCiccio, T. J., Efron B. (1996). Bootstrap confidence intervals. Statistical Science, 11, 189–228.
- Efron, B., Tibshirani, R. J. (1993). An Introduction to the Bootstrap. Chapman and Hall, New York.
- Kakade, C. S., Shirke, D. T., Kundu, D. (2008). Inference for P(Y < X) in Exponentiated Gumbel Distribution. Journal of Statistics and Applications, 3, 121–133.
- Kang, S. B., Seo, J. I., Kim, Y. (2013). An Analysis of Record Statistics based on an Exponentiated Gumbel Model. Communications for Statistical Applications and Methods, 20, 405–416.
- Kotz, S., Nadarajah, S. (2000). Extreme Value Distributions: Theory and Applications. Imperial College Press: London.
- Kotz, S., Lumelskii, Y., Pensky, M. (2003). The Stress-strength Model and its Generalizations: Theory and Applications. World Scientific.
- Lehmann, E. L. (1999). Elements of Large Sample Theory. Springer.
- Nadarajah, S. (2005). The exponentiated Gumbel distribution with climate application. Environmetrics, 17, 13–23.
Abstract
References
- Abdi, M. (2014). Confidence interval for the two-parameter exponentiated Gumbel distribution based on record values. International Journal of Applied Operational Research, 4, 73–80.
- Ahsanullah, M. (2004). Record Values. University Press of America Inc., Lanham, Maryland, USA : Theory and Applications.
- Arnold, B. C., Balakrishnan, N., and Nagaraja, H.N. (1998). Records. Wiley.
- Chen, Ming-Hui., Shao, Qi-Man. (1999). Monte Carlo estimation of Bayesian credible and HPD intervals. Journal of Computational and Graphical Statistics, 8, 69–92.
- DiCiccio, T. J., Efron B. (1996). Bootstrap confidence intervals. Statistical Science, 11, 189–228.
- Efron, B., Tibshirani, R. J. (1993). An Introduction to the Bootstrap. Chapman and Hall, New York.
- Kakade, C. S., Shirke, D. T., Kundu, D. (2008). Inference for P(Y < X) in Exponentiated Gumbel Distribution. Journal of Statistics and Applications, 3, 121–133.
- Kang, S. B., Seo, J. I., Kim, Y. (2013). An Analysis of Record Statistics based on an Exponentiated Gumbel Model. Communications for Statistical Applications and Methods, 20, 405–416.
- Kotz, S., Nadarajah, S. (2000). Extreme Value Distributions: Theory and Applications. Imperial College Press: London.
- Kotz, S., Lumelskii, Y., Pensky, M. (2003). The Stress-strength Model and its Generalizations: Theory and Applications. World Scientific.
- Lehmann, E. L. (1999). Elements of Large Sample Theory. Springer.
- Nadarajah, S. (2005). The exponentiated Gumbel distribution with climate application. Environmetrics, 17, 13–23.
Details
| Primary Language | English |
|---|---|
| Journal Section | Research Article |
| Authors | |
| Acceptance Date | December 17, 2013 |
| Publication Date | December 31, 2013 |
| Published in Issue | Year 2013 Volume: 6 Issue: 3 |