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Estimation Of Pr(X>Y) For Exponentiated Gumbel Distribution Based On Lower Record Values

Yıl 2013, Cilt: 6 Sayı: 3, 103 - 109, 31.12.2013

Öz

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. 

Kaynakça

  • 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.
Yıl 2013, Cilt: 6 Sayı: 3, 103 - 109, 31.12.2013

Öz

Kaynakça

  • 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.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Bahman Tarvirdizade

Yayımlanma Tarihi 31 Aralık 2013
Kabul Tarihi 17 Aralık 2013
Yayımlandığı Sayı Yıl 2013 Cilt: 6 Sayı: 3

Kaynak Göster

APA Tarvirdizade, B. (2013). Estimation Of Pr(X>Y) For Exponentiated Gumbel Distribution Based On Lower Record Values. Istatistik Journal of The Turkish Statistical Association, 6(3), 103-109.
AMA Tarvirdizade B. Estimation Of Pr(X>Y) For Exponentiated Gumbel Distribution Based On Lower Record Values. IJTSA. Aralık 2013;6(3):103-109.
Chicago Tarvirdizade, Bahman. “Estimation Of Pr(X>Y) For Exponentiated Gumbel Distribution Based On Lower Record Values”. Istatistik Journal of The Turkish Statistical Association 6, sy. 3 (Aralık 2013): 103-9.
EndNote Tarvirdizade B (01 Aralık 2013) Estimation Of Pr(X>Y) For Exponentiated Gumbel Distribution Based On Lower Record Values. Istatistik Journal of The Turkish Statistical Association 6 3 103–109.
IEEE B. Tarvirdizade, “Estimation Of Pr(X>Y) For Exponentiated Gumbel Distribution Based On Lower Record Values”, IJTSA, c. 6, sy. 3, ss. 103–109, 2013.
ISNAD Tarvirdizade, Bahman. “Estimation Of Pr(X>Y) For Exponentiated Gumbel Distribution Based On Lower Record Values”. Istatistik Journal of The Turkish Statistical Association 6/3 (Aralık 2013), 103-109.
JAMA Tarvirdizade B. Estimation Of Pr(X>Y) For Exponentiated Gumbel Distribution Based On Lower Record Values. IJTSA. 2013;6:103–109.
MLA Tarvirdizade, Bahman. “Estimation Of Pr(X>Y) For Exponentiated Gumbel Distribution Based On Lower Record Values”. Istatistik Journal of The Turkish Statistical Association, c. 6, sy. 3, 2013, ss. 103-9.
Vancouver Tarvirdizade B. Estimation Of Pr(X>Y) For Exponentiated Gumbel Distribution Based On Lower Record Values. IJTSA. 2013;6(3):103-9.