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Comparison of Estimators for Stress-Strength Reliability in the Gompertz Case

Year 2009, Volume: 38 Issue: 3, 339 - 349, 01.03.2009

References

  • Awad, A. M. and Gharraf, M. K. Estimation of P (Y < X) in the Burr case: A comparative study, Commun. Statist. Simul. Comp. 15 (2), 389–403, 1986.
  • Birnbaum, Z. W., 1956. On a use of the Mann-Whitney statistic (Proceedings of the Third Berkeley Symposium Math. Statistic Probability I, 1956), 13–17.
  • Chao, A. On comparing estimators of P (Y < X) in the exponential case, IEEE Trans. Reliab. 31 (4), 389–392, 1982.
  • Church, J. D. and Harris, B. The estimation of reliability from stress strength relationships, Technometrics 12, 49–54, 1970.
  • Constantine, K. and Karson, M. Estimators of P (Y < X) in the gamma case, Commun. Statist. Simul. Comp. 15, 365–388, 1986.
  • Ismail, A. A. On the optimal design of step-stress partially accelerated life tests for the Gompertz distribution with type-I censoring, 2006.
  • http://interstat.statjournals.net/articles/0606001.pdf
  • Jaheen, Z. F. A Bayesian analysis of record statistics from the Gompertz model, Appl. Math. Comp. 145 (2-3), 307–320, 2003.
  • Khedhairi, A. and Gohary, A. E. A new class of bivariate Gompertz distributions and its mixture, Int. J. Math. Anal. 2 (5), 235–253, 2008.
  • Kotz, S., Lumelskii, Y. and Pensky, M. The Stress-Strength Model and its Generalizations: Theory and Applications(World Scientific Publishing, Singapore, 2003).
  • Kundu, D. and Gupta R. D. Estimation of P (Y < X) for the generalized exponential dis- tribution, Metrika 61 (3), 291–308, 2005.
  • Lumelski, Ya. P. and Sapoznikov, P. N. Unbiased estimators of probabilities densities, Theor. Veroyat. Primen. 14, 372–380, 1969.
  • Mokhlis, N. A. Reliability of a stress-strength model with Burr Type III distributions, Com- mun. Statist.Theory Meth. 34 (7), 1643–1657, 2005.
  • Raqab M. Z. and Kundu, D. Comparison of different estimators of P (Y < X) for a scaled Burr type X distribution, Commun. Statist. Simul. Comp. 34 (2), 465–483, 2005.
  • Sara¸co˘glu, B. and Kaya, M. F. Maximum likelihood estimation and confidence intervals of system reliability for Gompertz distribution in stress-strength models, Sel¸cuk J. Appl. Math. 8(2), 25–36, 2007.
  • Surles, J. G. and Padgett, W. J. Inference for reliability and stress-strength for a scaled Burr-type X distribution, Lifetime Data Analy. 7, 187–200, 2001.
  • Wu, S. J., Chang, C. T. and Tsai, T. R. Point and interval estimations for the Gompertz distribution under progressive type-II censoring, Metron - International J. Stat. LXI (3), 403–418, 2003.
  • Wu, J. W., Hung, W. L. and Tsai, C. H. Estimation of parameters of the Gompertz distri- bution using the least squares method, Appl. Math. Comp. 158 (1), 133–147, 2004.
  • Wu, C. C., Wu, S. F. and Chan, H. Y. MLE and the estimated expected test time for the two-parameter Gompertz distribution under progressive censoring with binomial removals, Appl. Math. Comp. 181 (2), 1657–1670, 2006.

Comparison of Estimators for Stress-Strength Reliability in the Gompertz Case

Year 2009, Volume: 38 Issue: 3, 339 - 349, 01.03.2009

References

  • Awad, A. M. and Gharraf, M. K. Estimation of P (Y < X) in the Burr case: A comparative study, Commun. Statist. Simul. Comp. 15 (2), 389–403, 1986.
  • Birnbaum, Z. W., 1956. On a use of the Mann-Whitney statistic (Proceedings of the Third Berkeley Symposium Math. Statistic Probability I, 1956), 13–17.
  • Chao, A. On comparing estimators of P (Y < X) in the exponential case, IEEE Trans. Reliab. 31 (4), 389–392, 1982.
  • Church, J. D. and Harris, B. The estimation of reliability from stress strength relationships, Technometrics 12, 49–54, 1970.
  • Constantine, K. and Karson, M. Estimators of P (Y < X) in the gamma case, Commun. Statist. Simul. Comp. 15, 365–388, 1986.
  • Ismail, A. A. On the optimal design of step-stress partially accelerated life tests for the Gompertz distribution with type-I censoring, 2006.
  • http://interstat.statjournals.net/articles/0606001.pdf
  • Jaheen, Z. F. A Bayesian analysis of record statistics from the Gompertz model, Appl. Math. Comp. 145 (2-3), 307–320, 2003.
  • Khedhairi, A. and Gohary, A. E. A new class of bivariate Gompertz distributions and its mixture, Int. J. Math. Anal. 2 (5), 235–253, 2008.
  • Kotz, S., Lumelskii, Y. and Pensky, M. The Stress-Strength Model and its Generalizations: Theory and Applications(World Scientific Publishing, Singapore, 2003).
  • Kundu, D. and Gupta R. D. Estimation of P (Y < X) for the generalized exponential dis- tribution, Metrika 61 (3), 291–308, 2005.
  • Lumelski, Ya. P. and Sapoznikov, P. N. Unbiased estimators of probabilities densities, Theor. Veroyat. Primen. 14, 372–380, 1969.
  • Mokhlis, N. A. Reliability of a stress-strength model with Burr Type III distributions, Com- mun. Statist.Theory Meth. 34 (7), 1643–1657, 2005.
  • Raqab M. Z. and Kundu, D. Comparison of different estimators of P (Y < X) for a scaled Burr type X distribution, Commun. Statist. Simul. Comp. 34 (2), 465–483, 2005.
  • Sara¸co˘glu, B. and Kaya, M. F. Maximum likelihood estimation and confidence intervals of system reliability for Gompertz distribution in stress-strength models, Sel¸cuk J. Appl. Math. 8(2), 25–36, 2007.
  • Surles, J. G. and Padgett, W. J. Inference for reliability and stress-strength for a scaled Burr-type X distribution, Lifetime Data Analy. 7, 187–200, 2001.
  • Wu, S. J., Chang, C. T. and Tsai, T. R. Point and interval estimations for the Gompertz distribution under progressive type-II censoring, Metron - International J. Stat. LXI (3), 403–418, 2003.
  • Wu, J. W., Hung, W. L. and Tsai, C. H. Estimation of parameters of the Gompertz distri- bution using the least squares method, Appl. Math. Comp. 158 (1), 133–147, 2004.
  • Wu, C. C., Wu, S. F. and Chan, H. Y. MLE and the estimated expected test time for the two-parameter Gompertz distribution under progressive censoring with binomial removals, Appl. Math. Comp. 181 (2), 1657–1670, 2006.
There are 19 citations in total.

Details

Primary Language Turkish
Journal Section Mathematics
Authors

Bugra Saraçoglu This is me

M.f. Kaya This is me

A.m. Abd-elfattah This is me

Publication Date March 1, 2009
Published in Issue Year 2009 Volume: 38 Issue: 3

Cite

APA Saraçoglu, B., Kaya, M., & Abd-elfattah, A. (2009). Comparison of Estimators for Stress-Strength Reliability in the Gompertz Case. Hacettepe Journal of Mathematics and Statistics, 38(3), 339-349.
AMA Saraçoglu B, Kaya M, Abd-elfattah A. Comparison of Estimators for Stress-Strength Reliability in the Gompertz Case. Hacettepe Journal of Mathematics and Statistics. March 2009;38(3):339-349.
Chicago Saraçoglu, Bugra, M.f. Kaya, and A.m. Abd-elfattah. “Comparison of Estimators for Stress-Strength Reliability in the Gompertz Case”. Hacettepe Journal of Mathematics and Statistics 38, no. 3 (March 2009): 339-49.
EndNote Saraçoglu B, Kaya M, Abd-elfattah A (March 1, 2009) Comparison of Estimators for Stress-Strength Reliability in the Gompertz Case. Hacettepe Journal of Mathematics and Statistics 38 3 339–349.
IEEE B. Saraçoglu, M. Kaya, and A. Abd-elfattah, “Comparison of Estimators for Stress-Strength Reliability in the Gompertz Case”, Hacettepe Journal of Mathematics and Statistics, vol. 38, no. 3, pp. 339–349, 2009.
ISNAD Saraçoglu, Bugra et al. “Comparison of Estimators for Stress-Strength Reliability in the Gompertz Case”. Hacettepe Journal of Mathematics and Statistics 38/3 (March 2009), 339-349.
JAMA Saraçoglu B, Kaya M, Abd-elfattah A. Comparison of Estimators for Stress-Strength Reliability in the Gompertz Case. Hacettepe Journal of Mathematics and Statistics. 2009;38:339–349.
MLA Saraçoglu, Bugra et al. “Comparison of Estimators for Stress-Strength Reliability in the Gompertz Case”. Hacettepe Journal of Mathematics and Statistics, vol. 38, no. 3, 2009, pp. 339-4.
Vancouver Saraçoglu B, Kaya M, Abd-elfattah A. Comparison of Estimators for Stress-Strength Reliability in the Gompertz Case. Hacettepe Journal of Mathematics and Statistics. 2009;38(3):339-4.