×

Parameter estimations for generalized exponential distribution under progressive type-I interval censoring. (English) Zbl 1284.62595

Summary: The estimates, via maximum likelihood, moment method and probability plot, of the parameters in the generalized exponential distribution under progressive type-I interval censoring are studied. A simulation is conducted to compare these estimates in terms of mean squared errors and biases. Finally, these estimate methods are applied to a real data set based on patients with plasma cell myeloma in order to demonstrate the applicabilities.

MSC:

62N01 Censored data models
62P10 Applications of statistics to biology and medical sciences; meta analysis

Software:

R
Full Text: DOI

References:

[1] Aggarwala, R., Progressively interval censoring: Some mathematical results with application to inference, Communications in Statistics-Theory and Methods, 30, 1921-1935 (2001) · Zbl 0991.62079
[2] Balakrishnan, N.; Aggarwala, Rita, Progressive Censoring: Theory, Methods and Applications (2000), Birkhauser: Birkhauser Boston
[3] Carbone, P. P.; Kellerhouse, L. E.; Gehan, E. A., Plasmacytic myeloma: A study of the relationship of survival to various clinical manifestations and anomalous protein type in 112 patients, The American Journal of Medince, 42, 937-948 (1967)
[4] Carrasco, J. M.F.; Ortega, E. M.M.; Corderio, G. M., A generalized modified Weibull distribution for lifetime modeling, Computational Statistics and Data Analysis, 53, 450-462 (2008) · Zbl 1231.62015
[5] Colosimo, E. A.; Silva, A. F.; Cruz, F. R.B., Bias evaluation in the proportional hazards model, Journal of Statistical Computation and Simulation, 65, 3, 191-201 (2000) · Zbl 0977.62102
[6] Dempster; Laird; Rubin, Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society. Series B, 39, 1, 1-38 (1977) · Zbl 0364.62022
[7] Gupta, R. D.; Kundu, D., Generalized exponential distributions, Australian and New Zealand Journal of Statistics, 41, 173-188 (1999) · Zbl 1007.62503
[8] Gupta, R. D.; Kundu, D., Exponentiated exponential distribution: An alternative to gamma and Weibull distributions, Biometrical Journal, 43, 117-130 (2001) · Zbl 0997.62076
[9] Gupta, R. D.; Kundu, D., Generalized exponential distributions: Different method of estimations, Journal of Statistical Computation and Simulation, 69, 315-338 (2001) · Zbl 1007.62011
[10] Gupta, R. D.; Kundu, D., Generalized exponential distributions: Statistical inferences, Journal Statistic Theory Application, 1, 101-118 (2002), (Biometrical Journal, 43 117-130)
[11] Gupta, R. D.; Kundu, D., Discriminating between Weibull and generalized exponential distributions, Computational Statistics and Data Analysis, 43, 179-196 (2003) · Zbl 1429.62060
[12] Gupta, R. D.; Kundu, D., Generalized exponential distribution: Existing results and some recent developments, Journal of Statistical Planning and Inference, 137, 3537-3547 (2007) · Zbl 1119.62011
[13] Ihaka, R.; Gentleman, R., R: A language for data analysis and graphics, Journal of Computational and Graphical Statistics, 5, 299-314 (1996)
[14] Jaheen, Z. F., Empirical Bayes inference for generalized exponential distribution based on records, Communications in Statistics-Theory and Methods, 33, 1851-1861 (2004) · Zbl 1213.62014
[15] Kemp, C. D.; Kemp, W., Rapid generation of frequency tables, Applied Statistics, 36, 277-282 (1987)
[16] Kundu, D.; Rakab, M. Z., Generalized Rayleigh distribution: Different methods of estimation, Computational Statistics and Data Analysis, 49, 187-200 (2005) · Zbl 1429.62449
[17] Lai, C. D.; Xie, M.; Murthy, D. N.P., A modified Weibull distribution, IEEE Transactions on Reliability, 52, 33-37 (2003)
[18] Lawless, J., Statistical Models and Methods for Lifetime Data (1982), John Wiley and Sons: John Wiley and Sons New York · Zbl 0541.62081
[19] Montenegro, L. C.C.; Colosimo, E. A.; Cordeiro, G. M.; Cruz, F. R.B., Bias coorection in the Cox regression model, Journal of Statistical Computation and Simulation, 74, 5, 379-386 (2004) · Zbl 1060.62110
[20] Mudholkar, G. S.; Srivastava, D. K., Exponentiated Weibull family for analyzing bathtub failure data, IEEE Transactions on Reliability, 42, 299-302 (1993) · Zbl 0800.62609
[21] Mudholkar, G. S.; Srivastava, D. K.; Friemer, M., The exponentiated Weibull family: A reanalysis of the bus-motor-failure data, Technometrics, 37, 436-445 (1995) · Zbl 0900.62531
[22] Mudholkar, G. S.; Srivastava, D. K.; Kollia, G. D., A generalization of the Weibull distribution with application to the analysis of survival data, Journal of the American Statistical Association, 91, 1575-1583 (1996) · Zbl 0881.62017
[23] 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
[25] A language and environment for statistical computing (2006), R Foundation for Statistical Computing: R Foundation for Statistical Computing Vienna, Austria
[26] Raqab, M. Z.; Ahsanullah, M., Estimation of the location and scale parameters of generalized exponential distribution based on order statistics, Journal of Statistical Computation and Simulation, 69, 109-124 (2001) · Zbl 1151.62309
[27] Raqab, M. Z.; Madi, M. T., Bayesian inference for the generalized exponential distribution, Journal of Statistical Computation and Simulation, 75, 841-852 (2005) · Zbl 1076.62025
[28] Sarhan, A. M., Analysis of incomplete, censored data in competing risks models with generalized exponential distributions, IEEE Transactions on Reliability, 56, 1, 132-138 (2007)
[29] Wang, Z.; Desmond, A. F.; Lu, X., Modified censored moment estimation for the two-parameter Birnbaum-Saunders distribution, Computational Statistics and Data Analysis, 50, 1033-1051 (2006) · Zbl 1431.62467
[30] Zheng, G., Fisher information matrix in type-II censored data from exponentiated exponential family, Biometrical Journal, 44, 353-357 (2002) · Zbl 1441.62552
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.