Parameter estimations for generalized exponential distribution under progressive type-I interval censoring

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.

[1]  A. W. Kemp,et al.  Rapid Generation of Frequency Tables , 1987 .

[2]  Deo Kumar Srivastava,et al.  The exponentiated Weibull family: a reanalysis of the bus-motor-failure data , 1995 .

[3]  G. M. Cordeiro,et al.  Bias correction in the cox regression model , 2004 .

[4]  Debasis Kundu,et al.  On progressively censored generalized exponential distribution , 2009 .

[5]  Zhihui Wang,et al.  Modified censored moment estimation for the two-parameter Birnbaum-Saunders distribution , 2006, Comput. Stat. Data Anal..

[6]  Ross Ihaka,et al.  Gentleman R: R: A language for data analysis and graphics , 1996 .

[7]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[8]  G. S. Mudholkar,et al.  A Generalization of the Weibull Distribution with Application to the Analysis of Survival Data , 1996 .

[9]  G. S. Mudholkar,et al.  Exponentiated Weibull family for analyzing bathtub failure-rate data , 1993 .

[10]  Hon Keung Tony Ng,et al.  Statistical estimation for the parameters of Weibull distribution based on progressively type-I interval censored sample , 2009 .

[11]  Debasis Kundu,et al.  Discriminating between Weibull and generalized exponential distributions , 2003, Comput. Stat. Data Anal..

[12]  Ammar M. Sarhan,et al.  Analysis of Incomplete, Censored Data in Competing Risks Models With Generalized Exponential Distributions , 2007, IEEE Transactions on Reliability.

[13]  Debasis Kundu,et al.  Generalized Rayleigh distribution: different methods of estimations , 2005, Comput. Stat. Data Anal..

[14]  Jerald F. Lawless,et al.  Statistical Models and Methods for Lifetime Data. , 1983 .

[15]  D. Kundu,et al.  EXPONENTIATED EXPONENTIAL FAMILY: AN ALTERNATIVE TO GAMMA AND WEIBULL DISTRIBUTIONS , 2001 .

[16]  N. Balakrishnan,et al.  Progressive Censoring: Theory, Methods, and Applications , 2000 .

[17]  Rita Aggarwala,et al.  PROGRESSIVE INTERVAL CENSORING: SOME MATHEMATICAL RESULTS WITH APPLICATIONS TO INFERENCE , 2001 .

[18]  D. Kundu,et al.  Theory & Methods: Generalized exponential distributions , 1999 .

[19]  Debasis Kundu,et al.  Generalized exponential distribution: Existing results and some recent developments , 2007 .

[20]  E. Cramer.  Balakrishnan, Narayanaswamy ; Aggarwala, Rita: Progressive censoring : theory, methods, and applications / N. Balakrishnan ; Rita Aggarwala. - Boston ; Basel ; Berlin, 2000 , 2000 .

[21]  J. Lawless.  Statistical Models and Methods for Lifetime Data , 2002 .

[22]  E. Gehan,et al.  Plasmacytic myeloma. A study of the relationship of survival to various clinical manifestations and anomalous protein type in 112 patients. , 1967, The American journal of medicine.

[23]  Mohamed T. Madi,et al.  Bayesian inference for the generalized exponential distribution , 2005 .

[24]  Gauss M. Cordeiro,et al.  A generalized modified Weibull distribution for lifetime modeling , 2008 .

[25]  Gang Zheng.  On the Fisher information matrix in Type II censored data from the exponentiated exponential family , 2002 .

[26]  E. Colosimo,et al.  Bias evaluation in the proportional hazards model , 2000 .

[27]  D. N. Prabhakar Murthy,et al.  A modified Weibull distribution , 2003, IEEE Trans. Reliab..

[28]  Debasis Kundu,et al.  Generalized exponential distribution: different method of estimations , 2001 .

[29]  Z. F. Jaheen.  Empirical Bayes Inference for Generalized Exponential Distribution Based on Records , 2004 .

[30]  M. Ahsanullah,et al.  Estimation of the location and scale parameters of generalized exponential distribution based on order statistics , 2001 .