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Year 2022, Volume: 14 Issue: 2, 74 - 86, 31.12.2022

Çağatay Çetinkaya

Abstract

References

  • Abramowitz, M. and Stagun, I. (1964). Handbook of Special Functions. National Bureau of Standards, Dover Publications, New York.
  • Ahmed, E.A. (2014). Bayesian estimation based on progressive Type-II censoring from two-parameter bathtub-shaped lifetime model: an Markov chain Monte Carlo approach. Journal of Applied Statistics, 41(4), 752-768.
  • Chen, M.H. and Shao, Q.M. (1999). Monte Carlo estimation of Bayesian credible and HPD intervals. Journal of Computational and Graphical Statistics, 8(1), 69-92.
  • Chen, Z. (2000). A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function. Statistics & Probability Letters, 49(2), 155-161.
  • Congdon, P. (2006). Bayesian Statistical Modelling. Second edition, John Wiley & Sons, England.
  • Core Team, R. (2021). R: A language and environment for statistical computing. R Foundation for statistical computing, Vienna. https://www.R-project.org
  • Curtis, S.M., Goldin, I. and Evangelou, E. (2018). Package ‘mcmcplots’ [computer software]. R package version 0.4.3.
  • Fisher, R.A. (1930). Inverse Probability. Proceedings of the Cambridge Philosophical Society, xxvi, 528- 535.
  • Hand, D.J., Daly, F., McConway, K., Lunn, D. and Ostrowski, E. (1993). A handbook of small data sets. First edition, CRC Press, Boca Raton.
  • Hannig, J. (2013). Generalized fiducial inference via discretization. Statistica Sinica. 23(2), 489-514.
  • Hannig, J. (2009). On generalized fiducial inference. Statistica Sinica, 19(2), 491-544.
  • Hannig, J., Iyer, H., Lai, R.C. and Lee, T.C. (2016). Generalized fiducial inference: A review and new results. Journal of the American Statistical Association, 111(515), 1346-1361.
  • Kayal, T., Tripathi, Y.M. and Wang, L. (2019). Inference for the Chen distribution under progressive first-failure censoring. Journal of Statistical Theory and Practice, 13(4), 1-27.
  • Kayal, T., Tripathi, Y.M., Singh, D. P. and Rastogi, M.K. (2017). Estimation and prediction for Chen distribution with bathtub shape under progressive censoring. Journal of Statistical Computation and Simulation, 87(2), 348-366.
  • Li, Y. and Xu, A. (2016). Fiducial inference for Birnbaum-Saunders distribution. Journal of Statistical Computation and Simulation, 86(9), 1673-1685.
  • Mazucheli, J. and Mazucheli, M.J. (2017). Package ‘mle. tools’.
  • O’Reilly, F. and Rueda, R. (2007). Fiducial inferences for the truncated exponential distribution. Communications in Statistics - Theory and Methods, 36(12), 2207-2212.
  • Rastogi, M.K. and Tripathi, Y.M. (2013). Estimation using hybrid censored data from a two-parameter distribution with bathtub shape. Computational Statistics & Data Analysis, 67, 268-281.
  • Sarhan, A.M., Hamilton, D.C. and Smith, B. (2012). Parameter estimation for a two-parameter bathtubshaped lifetime distribution. Applied Mathematical Modelling, 36(11), 5380-5392.
  • Tierney, L. (1994) Markov chains for exploring posterior distributions. The Annals of Statistics, 22(4), 1701-1728.
  • Wandler, D.V. and Hannig, J. (2011). Fiducial inference on the largest mean of a multivariate normal distribution. Journal of Multivariate Analysis, 102(1), 87-104.
  • Wandler, D.V. and Hannig, J. (2012). Generalized fiducial confidence intervals for extremes. Extremes, 15, 67-87.
  • Wang, C.M., Hannig, J. and Iyer, H.K. (2012). Fiducial prediction intervals. Journal of Statistical Planning and Inference, 142(7), 1980-1990.
  • Weeranhandi, S. (1993). Generalized confidence intervals. Journal of the American Statistical Association, 88, 899-905.
  • Wu, J.W., Lu, H.L., Chen, C.H. and Wu, C.H. (2004). Statistical inference about the shape parameter of the new two-parameter bathtub-shaped lifetime distribution. Quality and Reliability Engineering International, 20(6), 607-616.
  • Wu, S.J. (2008). Estimation of the two-parameter bathtub-shaped lifetime distribution with progressive censoring. Journal of Applied Statistics, 35(10), 1139-1150.
  • Yan, L. and Liu, X. (2018). Generalized fiducial inference for generalized exponential distribution. Journal of Statistical Computation and Simulation, 88(7), 1369-1381.
  • Zabell, S. L. (1992). R.A. Fisher and fiducial argument. Statistical Science, 369-387.
  • Zhang, Z. (2014). WebBUGS: Conducting Bayesian statistical analysis online. Journal of Statistical Software, 61(1), 1-30.

Generalized Fiducial Inference for the Chen Distribution

Year 2022, Volume: 14 Issue: 2, 74 - 86, 31.12.2022

Çağatay Çetinkaya

Abstract

The fiducial inference idea was firstly proposed by Fisher [8] as a powerful method in statistical inference. Many authors such as Weeranhandi [24] and Hannig et. al. [12] improved this method from different points of view. Since the Bayesian method has some deficiencies such as assuming a prior distribution when there was little or no information about the parameters, the fiducial inference is used to overcome these adversities. This study deals with the generalized fiducial inference for the shape parameters of the Chen’s two-parameter lifetime distribution with bathtub shape or increasing failure rate [4]. The method based on the inverse of the structural equation which is proposed by Hannig et. al. [12] is used. We propose the generalized fiducial inferences of the parameters with their confidence intervals. Then, these estimations are compared with their maximum likelihood and Bayesian estimations. Simulation results show that the generalized fiducial inference is more applicable than the other methods in terms of the performances of estimators for the shape parameters of the Chen distribution. Finally, a real data example is used to illustrate the theoretical outcomes of these estimation procedures

Keywords

Bayesian Inference Generalized fiducial inference Interval estimation Chen distribution Point Estimation

References

  • Abramowitz, M. and Stagun, I. (1964). Handbook of Special Functions. National Bureau of Standards, Dover Publications, New York.
  • Ahmed, E.A. (2014). Bayesian estimation based on progressive Type-II censoring from two-parameter bathtub-shaped lifetime model: an Markov chain Monte Carlo approach. Journal of Applied Statistics, 41(4), 752-768.
  • Chen, M.H. and Shao, Q.M. (1999). Monte Carlo estimation of Bayesian credible and HPD intervals. Journal of Computational and Graphical Statistics, 8(1), 69-92.
  • Chen, Z. (2000). A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function. Statistics & Probability Letters, 49(2), 155-161.
  • Congdon, P. (2006). Bayesian Statistical Modelling. Second edition, John Wiley & Sons, England.
  • Core Team, R. (2021). R: A language and environment for statistical computing. R Foundation for statistical computing, Vienna. https://www.R-project.org
  • Curtis, S.M., Goldin, I. and Evangelou, E. (2018). Package ‘mcmcplots’ [computer software]. R package version 0.4.3.
  • Fisher, R.A. (1930). Inverse Probability. Proceedings of the Cambridge Philosophical Society, xxvi, 528- 535.
  • Hand, D.J., Daly, F., McConway, K., Lunn, D. and Ostrowski, E. (1993). A handbook of small data sets. First edition, CRC Press, Boca Raton.
  • Hannig, J. (2013). Generalized fiducial inference via discretization. Statistica Sinica. 23(2), 489-514.
  • Hannig, J. (2009). On generalized fiducial inference. Statistica Sinica, 19(2), 491-544.
  • Hannig, J., Iyer, H., Lai, R.C. and Lee, T.C. (2016). Generalized fiducial inference: A review and new results. Journal of the American Statistical Association, 111(515), 1346-1361.
  • Kayal, T., Tripathi, Y.M. and Wang, L. (2019). Inference for the Chen distribution under progressive first-failure censoring. Journal of Statistical Theory and Practice, 13(4), 1-27.
  • Kayal, T., Tripathi, Y.M., Singh, D. P. and Rastogi, M.K. (2017). Estimation and prediction for Chen distribution with bathtub shape under progressive censoring. Journal of Statistical Computation and Simulation, 87(2), 348-366.
  • Li, Y. and Xu, A. (2016). Fiducial inference for Birnbaum-Saunders distribution. Journal of Statistical Computation and Simulation, 86(9), 1673-1685.
  • Mazucheli, J. and Mazucheli, M.J. (2017). Package ‘mle. tools’.
  • O’Reilly, F. and Rueda, R. (2007). Fiducial inferences for the truncated exponential distribution. Communications in Statistics - Theory and Methods, 36(12), 2207-2212.
  • Rastogi, M.K. and Tripathi, Y.M. (2013). Estimation using hybrid censored data from a two-parameter distribution with bathtub shape. Computational Statistics & Data Analysis, 67, 268-281.
  • Sarhan, A.M., Hamilton, D.C. and Smith, B. (2012). Parameter estimation for a two-parameter bathtubshaped lifetime distribution. Applied Mathematical Modelling, 36(11), 5380-5392.
  • Tierney, L. (1994) Markov chains for exploring posterior distributions. The Annals of Statistics, 22(4), 1701-1728.
  • Wandler, D.V. and Hannig, J. (2011). Fiducial inference on the largest mean of a multivariate normal distribution. Journal of Multivariate Analysis, 102(1), 87-104.
  • Wandler, D.V. and Hannig, J. (2012). Generalized fiducial confidence intervals for extremes. Extremes, 15, 67-87.
  • Wang, C.M., Hannig, J. and Iyer, H.K. (2012). Fiducial prediction intervals. Journal of Statistical Planning and Inference, 142(7), 1980-1990.
  • Weeranhandi, S. (1993). Generalized confidence intervals. Journal of the American Statistical Association, 88, 899-905.
  • Wu, J.W., Lu, H.L., Chen, C.H. and Wu, C.H. (2004). Statistical inference about the shape parameter of the new two-parameter bathtub-shaped lifetime distribution. Quality and Reliability Engineering International, 20(6), 607-616.
  • Wu, S.J. (2008). Estimation of the two-parameter bathtub-shaped lifetime distribution with progressive censoring. Journal of Applied Statistics, 35(10), 1139-1150.
  • Yan, L. and Liu, X. (2018). Generalized fiducial inference for generalized exponential distribution. Journal of Statistical Computation and Simulation, 88(7), 1369-1381.
  • Zabell, S. L. (1992). R.A. Fisher and fiducial argument. Statistical Science, 369-387.
  • Zhang, Z. (2014). WebBUGS: Conducting Bayesian statistical analysis online. Journal of Statistical Software, 61(1), 1-30.
There are 29 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Çağatay Çetinkaya 0000-0001-8010-4261

Publication Date December 31, 2022
Acceptance Date September 23, 2022
Published in Issue Year 2022 Volume: 14 Issue: 2

Cite

APA Çetinkaya, Ç. (2022). Generalized Fiducial Inference for the Chen Distribution. Istatistik Journal of The Turkish Statistical Association, 14(2), 74-86.
AMA Çetinkaya Ç. Generalized Fiducial Inference for the Chen Distribution. IJTSA. December 2022;14(2):74-86.
Chicago Çetinkaya, Çağatay. “Generalized Fiducial Inference for the Chen Distribution”. Istatistik Journal of The Turkish Statistical Association 14, no. 2 (December 2022): 74-86.
EndNote Çetinkaya Ç (December 1, 2022) Generalized Fiducial Inference for the Chen Distribution. Istatistik Journal of The Turkish Statistical Association 14 2 74–86.
IEEE Ç. Çetinkaya, “Generalized Fiducial Inference for the Chen Distribution”, IJTSA, vol. 14, no. 2, pp. 74–86, 2022.
ISNAD Çetinkaya, Çağatay. “Generalized Fiducial Inference for the Chen Distribution”. Istatistik Journal of The Turkish Statistical Association 14/2 (December 2022), 74-86.
JAMA Çetinkaya Ç. Generalized Fiducial Inference for the Chen Distribution. IJTSA. 2022;14:74–86.
MLA Çetinkaya, Çağatay. “Generalized Fiducial Inference for the Chen Distribution”. Istatistik Journal of The Turkish Statistical Association, vol. 14, no. 2, 2022, pp. 74-86.
Vancouver Çetinkaya Ç. Generalized Fiducial Inference for the Chen Distribution. IJTSA. 2022;14(2):74-86.
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