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ESTIMATIONS FOR PROPORTIONAL REVERSED HAZARD RATE MODEL DISTRIBUTIONS BASED ON UPPER RECORD VALUES AND INTER-RECORD TIMES

Year 2014, Volume: 7 Issue: 2, 55 - 62, 01.06.2014

Fatih Kızılaslan Mustafa Nadar.

Abstract

The distributions from proportional reversed hazard rate models have been extensively studiedin literature because of their wide applicability in the modelling and analysis of lifetime data. Moreover,record values and their properties have also been examined by many authors. In this study, we consider thedistributions from the two-parameter proportional reversed hazard rate models. The maximum likelihoodand Bayes estimates are obtained for the unknown parameters based on upper record values with the numberof trials following the record values (inter-record times). These estimates are compared in terms of theestimated risk by the Monte Carlo simulations for the generalized Rayleigh (Burr Type X) distribution

Keywords

Bayes estimation Inter-record times PRHR model Record values

References

  • Ahmadi, J. and Doostparast, M. (2006). Bayesian estimation and prediction for some life distributions based on record values. Statistical Papers, 47(3), 373-392.
  • Asgharzadeh, A. and Fallah, A. (2011). Estimation and Prediction for Exponentiated Family of Distri- butions Based on Records. Communications in Statistics-Theory and Methods, 40, 68-83.
  • Wang, L. and Shi, Y. (2013). Reliability analysis of a class of exponential distribution under record values. Journal of Computational and Applied Mathematics, 239, 367-379.
  • Kızılaslan, F. and Nadar, M. (2013). Estimation with the generalized exponential distribution based on record values and inter-record times. Journal of Statistical Computation and Simulation, DOI:10.1080/00949655.2013.856910. [5] Arnold, B.C., Balakrishnan, N. and Nagaraja, H.N. (1998). Records. John Wiley & Sons, New York.
  • Lehmann, E.L. (1953). The power of rank tests. Annals of Mathematical Statistics, 24, 28-43.
  • Shakil, M. and Ahsanullah, M. (2012). Review on Order Statistics and Record Values from FαDistri- butions. Pakistan Journal of Statistics and Operation Research, 8(1), 101-120.
  • Hofmann, G. and Nagaraja, H.N. (2003). Fisher information in record data. Metrika, 57, 177-193.
  • Varian, H.R. (1975). A Bayesian approach to real estate assessment, In: Finberg S.E., Zellner A. (eds) Studies in Bayesian econometrics and statistics in honour of Leonard J. Savage, North Holland, Ams- terdam.
  • Soland, R.M. (1969). Bayesian analysis of the Weibull process with unknown scale and shape parameters. IEEE Transactions on Reliability, 18, 181-184.
  • Nadar, M. and Kızılaslan, F. (2014). Estimation and prediction of the Burr type XII distribution based on record values and inter-record times. Journal of Statistical Computation and Simulation, DOI:10.1080/00949655.2014.970554.

Year 2014, Volume: 7 Issue: 2, 55 - 62, 01.06.2014

Fatih Kızılaslan Mustafa Nadar.

Abstract

References

  • Ahmadi, J. and Doostparast, M. (2006). Bayesian estimation and prediction for some life distributions based on record values. Statistical Papers, 47(3), 373-392.
  • Asgharzadeh, A. and Fallah, A. (2011). Estimation and Prediction for Exponentiated Family of Distri- butions Based on Records. Communications in Statistics-Theory and Methods, 40, 68-83.
  • Wang, L. and Shi, Y. (2013). Reliability analysis of a class of exponential distribution under record values. Journal of Computational and Applied Mathematics, 239, 367-379.
  • Kızılaslan, F. and Nadar, M. (2013). Estimation with the generalized exponential distribution based on record values and inter-record times. Journal of Statistical Computation and Simulation, DOI:10.1080/00949655.2013.856910. [5] Arnold, B.C., Balakrishnan, N. and Nagaraja, H.N. (1998). Records. John Wiley & Sons, New York.
  • Lehmann, E.L. (1953). The power of rank tests. Annals of Mathematical Statistics, 24, 28-43.
  • Shakil, M. and Ahsanullah, M. (2012). Review on Order Statistics and Record Values from FαDistri- butions. Pakistan Journal of Statistics and Operation Research, 8(1), 101-120.
  • Hofmann, G. and Nagaraja, H.N. (2003). Fisher information in record data. Metrika, 57, 177-193.
  • Varian, H.R. (1975). A Bayesian approach to real estate assessment, In: Finberg S.E., Zellner A. (eds) Studies in Bayesian econometrics and statistics in honour of Leonard J. Savage, North Holland, Ams- terdam.
  • Soland, R.M. (1969). Bayesian analysis of the Weibull process with unknown scale and shape parameters. IEEE Transactions on Reliability, 18, 181-184.
  • Nadar, M. and Kızılaslan, F. (2014). Estimation and prediction of the Burr type XII distribution based on record values and inter-record times. Journal of Statistical Computation and Simulation, DOI:10.1080/00949655.2014.970554.
There are 10 citations in total.

Details

Other ID JA35RZ22ZS
Journal Section Research Article
Authors

Fatih Kızılaslan This is me

Mustafa Nadar. This is me

Publication Date June 1, 2014
Published in Issue Year 2014 Volume: 7 Issue: 2

Cite

APA Kızılaslan, F., & Nadar., M. (2014). ESTIMATIONS FOR PROPORTIONAL REVERSED HAZARD RATE MODEL DISTRIBUTIONS BASED ON UPPER RECORD VALUES AND INTER-RECORD TIMES. Istatistik Journal of The Turkish Statistical Association, 7(2), 55-62.
AMA Kızılaslan F, Nadar. M. ESTIMATIONS FOR PROPORTIONAL REVERSED HAZARD RATE MODEL DISTRIBUTIONS BASED ON UPPER RECORD VALUES AND INTER-RECORD TIMES. IJTSA. June 2014;7(2):55-62.
Chicago Kızılaslan, Fatih, and Mustafa Nadar. “ESTIMATIONS FOR PROPORTIONAL REVERSED HAZARD RATE MODEL DISTRIBUTIONS BASED ON UPPER RECORD VALUES AND INTER-RECORD TIMES”. Istatistik Journal of The Turkish Statistical Association 7, no. 2 (June 2014): 55-62.
EndNote Kızılaslan F, Nadar. M (June 1, 2014) ESTIMATIONS FOR PROPORTIONAL REVERSED HAZARD RATE MODEL DISTRIBUTIONS BASED ON UPPER RECORD VALUES AND INTER-RECORD TIMES. Istatistik Journal of The Turkish Statistical Association 7 2 55–62.
IEEE F. Kızılaslan and M. Nadar., “ESTIMATIONS FOR PROPORTIONAL REVERSED HAZARD RATE MODEL DISTRIBUTIONS BASED ON UPPER RECORD VALUES AND INTER-RECORD TIMES”, IJTSA, vol. 7, no. 2, pp. 55–62, 2014.
ISNAD Kızılaslan, Fatih - Nadar., Mustafa. “ESTIMATIONS FOR PROPORTIONAL REVERSED HAZARD RATE MODEL DISTRIBUTIONS BASED ON UPPER RECORD VALUES AND INTER-RECORD TIMES”. Istatistik Journal of The Turkish Statistical Association 7/2 (June 2014), 55-62.
JAMA Kızılaslan F, Nadar. M. ESTIMATIONS FOR PROPORTIONAL REVERSED HAZARD RATE MODEL DISTRIBUTIONS BASED ON UPPER RECORD VALUES AND INTER-RECORD TIMES. IJTSA. 2014;7:55–62.
MLA Kızılaslan, Fatih and Mustafa Nadar. “ESTIMATIONS FOR PROPORTIONAL REVERSED HAZARD RATE MODEL DISTRIBUTIONS BASED ON UPPER RECORD VALUES AND INTER-RECORD TIMES”. Istatistik Journal of The Turkish Statistical Association, vol. 7, no. 2, 2014, pp. 55-62.
Vancouver Kızılaslan F, Nadar. M. ESTIMATIONS FOR PROPORTIONAL REVERSED HAZARD RATE MODEL DISTRIBUTIONS BASED ON UPPER RECORD VALUES AND INTER-RECORD TIMES. IJTSA. 2014;7(2):55-62.