×

Parameter estimations for mixed generalized exponential distribution based on progressive type-I interval censoring. (English) Zbl 1426.62294

Summary: This paper considers the estimation of parameters based on a progressively type-I interval-censored data from a mixed generalized exponential distribution. The maximum likelihood estimation is used but an analytic form cannot be obtained. The EM algorithm is applied to obtain the maximum likelihood estimates. The performance of the estimates is judged by a simulating study and a real data is presented to illustrate the method of estimation developed here.

MSC:

62N02 Estimation in survival analysis and censored data
62F10 Point estimation
62N01 Censored data models

References:

[1] Aggarwala, R., Progressive interval censoring: Some mathematical results with applications to inference, Communications in Statistics-Theory and Methods, 30, 1921-1935 (2001) · Zbl 0991.62079 · doi:10.1081/STA-100105705
[2] Balakrishnan, N.; Aggarwala, R., Progressive Censoring (2000), Boston, MA: Birkhauser, Boston, MA · doi:10.1007/978-1-4612-1334-5
[3] Balakrishnan, N.; Kannan, N.; Lin, C. T.; Wu, S. J., Inference for the extreme value distribution under progressive Type-II censoring, Journal of Statistical Computation and Simulation, 74, 25-45 (2004) · Zbl 1048.62090 · doi:10.1080/0094965031000105881
[4] Berkson, J.; Gage, R. P., Calculation of survival rates for cancer, Proceedings of the Staff Meetings Mayo Clinic, 25, 270-286 (1950)
[5] Chen, D. G.; Lio, Y. L., Parameter estimations for generalized exponential distribution under progressive type-I interval censoring, Computational Statistics and Data Analysis, 54, 1581-1591 (2010) · Zbl 1284.62595 · doi:10.1016/j.csda.2010.01.007
[6] Dempster, A. P.; Laird, N. M.; Rubin, D. B., Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society. Series B, 39, 1-38 (1977) · Zbl 0364.62022
[7] Lawless, J. F., Statistical models and methods for lifetime data (2003), Hoboken, NJ: John Wiley & Sons, Hoboken, NJ · Zbl 1015.62093
[8] Lin, C. T.; Wu, S. J. S.; Balakrishnan, N., Planning life tests with progressively type-I interval censored data from the lognormal distribution, Journal of Statistical Planning and Inference, 139, 54-61 (2009) · Zbl 1154.62074 · doi:10.1016/j.jspi.2008.05.016
[9] Lio, Y. Z.; Chen, D. G.; Tsai, T. R., Parameter estimations for generalized Rayleigh distribution under progressively type-I interval censored data, Open Journal of Statistics, 1, 46-57 (2011) · doi:10.4236/ojs.2011.12006
[10] Mcclean, S., Estimation for the mixed exponential distribution using grouped follow-up data, Journal of the Royal Statistical Society. Series C: Applied Statistics, 35, 31-37 (1986)
[11] Ng, H.; Wang, Z., Statistical estimation for the parameters of Weibull distribution based on progressively type-I interval censored sample, Journal of Statistical Computation and Simulation, 79, 145-159 (2009) · Zbl 1161.62066 · doi:10.1080/00949650701648822
[12] Peng, X.; Yan, Z., Parameter estimations with gamma distribution based on progressive type- I interval censoring, IEEE International Conference on Computer Science and Automation Engineering, 1, 449-453 (2011)
[13] Pradhan, B.; Gijo, E. V., Parameter estimation of lognormal distribution under progressive type-I interval censoring (2013)
[14] Soliman, A. A., Estimators for the finite mixture of Rayleigh model based on progressively censored data, Communications in Statistics-Theory and Methods, 35, 803-820 (2006) · Zbl 1093.62091 · doi:10.1080/03610920500501379
[15] Tian, Y.; He, J.; Chen, P., Mixed generalized exponential with censored data, Journal of Chongqing Institute of Technology (Natural Science), 22, 79-81 (2008)
[16] Tian, Y. Z.; Tian, M. Z. I.; Chen, P., Parameter estimation for a mixture of generalized exponential distribution under grouped and right-censored samples, Chinese Journal of Applied Probability and Statistics, 28, 561-571 (2012) · Zbl 1289.62110
[17] Tian, Y. Z.; Tian, M. Z.; Zhu, Q. Q., Estimating a finite mixed exponential distribution under progressively type-II censored data, Communications in Statistics-Theory and Methods, 43, 3762-3776 (2014) · Zbl 1302.62222 · doi:10.1080/03610926.2012.752843
[18] Tian, Y. Z.; Zhu, Q. Q.; Tian, M. Z., Inference for mixed generalized exponential distribution under progressively type-II censored samples, Journal of Applied Statistics, 41, 660-676 (2013) · Zbl 1514.62897
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.