Approximate MLE for the scale parameter of the generalized exponential distribution under random censoring

Abstract In this paper, we consider the maximum likelihood estimator (MLE) of the scale parameter of the generalized exponential (GE) distribution based on a random censoring model. We assume the censoring distribution also follows a GE distribution. Since the estimator does not provide an explicit solution, we propose a simple method of deriving an explicit estimator by approximating the likelihood function. In order to compare the performance of the estimators, Monte Carlo simulation is conducted. The results show that the MLE and the approximate MLE are almost identical in terms of bias and variance.

[1]  Ali A. Ismail.  Inference in the generalized exponential distribution under partially accelerated tests with progressive Type-II censoring , 2012 .

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

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

[4]  D. Kundu,et al.  Closeness of Gamma and Generalized Exponential Distribution , 2003 .

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

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

[7]  Gauss M. Cordeiro,et al.  The beta generalized exponential distribution , 2008, 0809.1889.

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

[9]  E. Kaplan,et al.  Nonparametric Estimation from Incomplete Observations , 1958 .

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

[11]  James A. Koziol,et al.  A Cramér-von Mises statistic for randomly censored data , 1976 .

[12]  Akbar Asgharzadeh.  Approximate MLE for the scaled generalized exponential distribution under progressive type-II censoring , 2009 .

[13]  Elisa T. Lee,et al.  Statistical Methods for Survival Data Analysis , 1994, IEEE Transactions on Reliability.

[14]  Debasis Kundu,et al.  Estimating the Parameters of the Generalized Exponential Distribution in Presence of Hybrid Censoring , 2009 .

[15]  N. Breslow,et al.  A Large Sample Study of the Life Table and Product Limit Estimates Under Random Censorship , 1974 .

[16]  Mohammad Z. Raqab,et al.  Inferences for generalized exponential distribution based on record statistics , 2002 .

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

[18]  Ahmad M. Alshamrani,et al.  The generalized Gompertz distribution , 2013 .

[19]  Eisa Mahmoudi,et al.  Generalized exponential-power series distributions , 2012, Comput. Stat. Data Anal..

[20]  Rupert G. Miller,et al.  Survival Analysis , 2022, The SAGE Encyclopedia of Research Design.

[21]  Narayanaswamy Balakrishnan.  Approximate MLE of the scale parameter of the Rayleigh distribution with censoring , 1989 .

[22]  D. Kundu,et al.  An extension of the generalized exponential distribution , 2011 .

[23]  Paul Meier,et al.  Estimation of a Distribution Function from Incomplete Observations , 1975, Journal of Applied Probability.

[24]  J. Lieblein,et al.  Statistical Investigation of the Fatigue Life of Deep-Groove Ball Bearings , 1956 .

[25]  B. Efron.  The two sample problem with censored data , 1967 .

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

[27]  M. Hollander,et al.  Small-Sample Results for the Kaplan-Meier Estimator , 1982 .

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

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

[30]  Emil Frei,et al.  The Effect of 6-Mercaptopurine on the Duration of Steroid-induced Remissions in Acute Leukemia: A Model for Evaluation of Other Potentially Useful Therapy , 1963 .

[31]  Sigmund J. Amster,et al.  The Statistical Treatment of Fatigue Experiments , 1964 .

[32]  Estimation of the scale parameter of the half-logistic distribution with multiply type II censored sample , 2011 .

[33]  Yuhlong Lio,et al.  Parameter estimations for generalized exponential distribution under progressive type-I interval censoring , 2010, Comput. Stat. Data Anal..