Year 2020,
, 29 - 36, 01.02.2020
Gülcan Gencer
,
Kerem Gencer
References
- [1] K. Cooray, “Analyzing grouped, censored, and truncated data using the odd weibull family”, Communications in Statistics - Theory and Methods, vol. 41 no.15, pp. 2661-2680, 2012.
- [2] K. Cooray, “A study of moments and likelihood estimators of the odd Weibull distribution”, Statistical Methodology, vol. 26, pp. 72-83, 2015.
- [3] H. Jiang , M. Xie and L.C. Tang, “On the odd Weibull distribution”, J. Risk and Reliability, vol. 222, pp. 583-594, 2008.
- [4] N. Balakrishnan, N. Kannan, C.T. Lin, and S. J. S. Wu, “Inference for the extreme value distribution under progressive type-II censoring”, J. Statist. Comput. Simul., vol. 74, pp. 25–45, 2004.
- [5] S.J. Wu, “Estimations of the Parameters of the Weibull Distributions With Progressively Censored Data”, J. Japan Statist. Soc., vol. 32 no. 2, pp. 155-163, 2002.
- [6] S.J. Wu, C.T. Chang and T.R. Tsai, “Point and Interval Estimations For The Gompertz Distribution Under Progressive Type II Censoring”, Metron-International Journal Of Statistics LXI, vol.3, pp. 409-418, 2003.
- [7] N. Balakrishnan, and R. Aggarwala, “Progressive Censoring: Theory, Methods and Applications”, Birkhauser, Boston, 2000.
- [8] N. Balakrishnan, “Progressive censoring methodology: an appraisal, (with discussions) Test”, vol. 16, no. 2, 211 – 296, 2007.
- [9] C.D. Lai, “Generalized Weibull Distributions”, London, Springer, pp. 63-65, 2014.
- [10] G.S. Mudholkar and D.K. Srivastava, “Exponentiated Weibull family for analyzing bathtub failure rate data”, IEEE Transactions on Reliability, vol.42, pp. 299-302, 1993.
- [11] G. Gencer and B. Saraçoğlu, “Comparison of approximate Bayes Estimators under different loss functions for parameters of Odd Weibull Distribution”, Journal of Selçuk University Natural and Applied Science, vol. 5, no.1, pp. 18-32, 2016.
- [12] S. Nadarajah, G.M. Cordeiro and E.M.M. Ortega, “Exponentiated Weibull Distribution: a survey”, Statistical Papers, vol. 54, no.3, pp.839-877, 2013.
- [13] A.M. Salem and O.E. Abo-Kasem, “Estimation for the Parameters of the Exponentiated Weibull Distribution Based on Progressive Hybrid Censored Samples”, Int. J. Contemp. Math. Sciences, vol. 6, no. 35, pp. 1713-1724, 2011.
- [14] M.M. Nassar and F.H. Eissa, “Bayesian estimation for the exponentiated Weibull model”, Communications in Statistics – Theory and Methods, vol.33, pp. 2343- 2362, 2004.
- [15] E.M.M. Ortega, G.M. Cordeiro, E.M. Hashimoto and K. Cooray, “A log-linear regression model for the odd Weibull distribution with censored data”, Journal of Applied Statistics, vol.41 no.9, pp.1859–1880, 2014.
- [16] Y.Y Abdelall, “The Odd Generalized Exponential Modified Weibull Distribution”, ınternational Mathematical Forum, vol.11, no.16, pp. 943-959, 2016.
- [17] M.Ç. Korkmaz, M. Alizadeh, H.M. Yousof and N.S. Butt, “The Generalized Odd Weibull Generated Family of Distributions: Statistical Properties and Applications”, Pakistan Journal of Statistics and Operation Research, vol.14, no.3, pp. 541-556, 2018.
- [18] M. Alizadeh, E. Altun, A.Z. Afify and G. Ozel, “The Extended Odd Weibull-G Family: Properties And Applıcatıons”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol.68 no.1, pp. 161-186, 2018.
- [19] K. Cooray, “Generalization of theWeibull distribution: the odd Weibull family”, Statistical Modelling, vol. 6, pp.265–277, 2006.
- [20] L. Tierney and J. B. Kadane, "Accurate Approximations for Posterior Moments and Marginal Densities", Journal of the American Statistical Association, vol.81, no.393, pp. 82-86, 1986.
- [21] N. Balakrishnan and R.A. Sandhu, “A Simple Simulation Algorithm for Generating Progressively Type-II Censored Sample”, American Statistician, vol.49, pp.229-230, 1995.
Estimations For The Odd Weibull Distribution under Progressive Type-II Right Censored Samples
Year 2020,
, 29 - 36, 01.02.2020
Gülcan Gencer
,
Kerem Gencer
Abstract
In this study, We introduced
performances Maximum Likelihood (ML) and Bayes estimation under LINEX, GENTROPY
and SQUARED loss functions results concerning a progressively type-II censored
samples for parameters of OddW distribution. We used obtain the Tierney Kadane’s
approximation to obtain bayesian estimates.
The Mean Squared Error (MSE)s of MLEs and (MSE)s
of bayes estimates under LINEX, GENTROPY and
SQUARED loss functions for unknown parameters
are computed using Monte Carlo simulation.
References
- [1] K. Cooray, “Analyzing grouped, censored, and truncated data using the odd weibull family”, Communications in Statistics - Theory and Methods, vol. 41 no.15, pp. 2661-2680, 2012.
- [2] K. Cooray, “A study of moments and likelihood estimators of the odd Weibull distribution”, Statistical Methodology, vol. 26, pp. 72-83, 2015.
- [3] H. Jiang , M. Xie and L.C. Tang, “On the odd Weibull distribution”, J. Risk and Reliability, vol. 222, pp. 583-594, 2008.
- [4] N. Balakrishnan, N. Kannan, C.T. Lin, and S. J. S. Wu, “Inference for the extreme value distribution under progressive type-II censoring”, J. Statist. Comput. Simul., vol. 74, pp. 25–45, 2004.
- [5] S.J. Wu, “Estimations of the Parameters of the Weibull Distributions With Progressively Censored Data”, J. Japan Statist. Soc., vol. 32 no. 2, pp. 155-163, 2002.
- [6] S.J. Wu, C.T. Chang and T.R. Tsai, “Point and Interval Estimations For The Gompertz Distribution Under Progressive Type II Censoring”, Metron-International Journal Of Statistics LXI, vol.3, pp. 409-418, 2003.
- [7] N. Balakrishnan, and R. Aggarwala, “Progressive Censoring: Theory, Methods and Applications”, Birkhauser, Boston, 2000.
- [8] N. Balakrishnan, “Progressive censoring methodology: an appraisal, (with discussions) Test”, vol. 16, no. 2, 211 – 296, 2007.
- [9] C.D. Lai, “Generalized Weibull Distributions”, London, Springer, pp. 63-65, 2014.
- [10] G.S. Mudholkar and D.K. Srivastava, “Exponentiated Weibull family for analyzing bathtub failure rate data”, IEEE Transactions on Reliability, vol.42, pp. 299-302, 1993.
- [11] G. Gencer and B. Saraçoğlu, “Comparison of approximate Bayes Estimators under different loss functions for parameters of Odd Weibull Distribution”, Journal of Selçuk University Natural and Applied Science, vol. 5, no.1, pp. 18-32, 2016.
- [12] S. Nadarajah, G.M. Cordeiro and E.M.M. Ortega, “Exponentiated Weibull Distribution: a survey”, Statistical Papers, vol. 54, no.3, pp.839-877, 2013.
- [13] A.M. Salem and O.E. Abo-Kasem, “Estimation for the Parameters of the Exponentiated Weibull Distribution Based on Progressive Hybrid Censored Samples”, Int. J. Contemp. Math. Sciences, vol. 6, no. 35, pp. 1713-1724, 2011.
- [14] M.M. Nassar and F.H. Eissa, “Bayesian estimation for the exponentiated Weibull model”, Communications in Statistics – Theory and Methods, vol.33, pp. 2343- 2362, 2004.
- [15] E.M.M. Ortega, G.M. Cordeiro, E.M. Hashimoto and K. Cooray, “A log-linear regression model for the odd Weibull distribution with censored data”, Journal of Applied Statistics, vol.41 no.9, pp.1859–1880, 2014.
- [16] Y.Y Abdelall, “The Odd Generalized Exponential Modified Weibull Distribution”, ınternational Mathematical Forum, vol.11, no.16, pp. 943-959, 2016.
- [17] M.Ç. Korkmaz, M. Alizadeh, H.M. Yousof and N.S. Butt, “The Generalized Odd Weibull Generated Family of Distributions: Statistical Properties and Applications”, Pakistan Journal of Statistics and Operation Research, vol.14, no.3, pp. 541-556, 2018.
- [18] M. Alizadeh, E. Altun, A.Z. Afify and G. Ozel, “The Extended Odd Weibull-G Family: Properties And Applıcatıons”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol.68 no.1, pp. 161-186, 2018.
- [19] K. Cooray, “Generalization of theWeibull distribution: the odd Weibull family”, Statistical Modelling, vol. 6, pp.265–277, 2006.
- [20] L. Tierney and J. B. Kadane, "Accurate Approximations for Posterior Moments and Marginal Densities", Journal of the American Statistical Association, vol.81, no.393, pp. 82-86, 1986.
- [21] N. Balakrishnan and R.A. Sandhu, “A Simple Simulation Algorithm for Generating Progressively Type-II Censored Sample”, American Statistician, vol.49, pp.229-230, 1995.