Inference for Burr XII distribution under Type I progressive hybrid censoring

ABSTRACT We consider estimation of unknown parameters of a Burr XII distribution based on progressively Type I hybrid censored data. The maximum likelihood estimates are obtained using an expectation maximization algorithm. Asymptotic interval estimates are constructed from the Fisher information matrix. We obtain Bayes estimates under the squared error loss function using the Lindley method and Metropolis–Hastings algorithm. The predictive estimates of censored observations are obtained and the corresponding prediction intervals are also constructed. We compare the performance of the different methods using simulations. Two real datasets have been analyzed for illustrative purposes.

[1]  D. Cox,et al.  An Analysis of Transformations , 1964 .

[2]  J. Bert Keats,et al.  The Burr XII Distribution in Reliability Analysis , 1998 .

[3]  Jerald F. Lawless,et al.  Statistical Models and Methods for Lifetime Data: Lawless/Statistical , 2002 .

[4]  R. Arabi Belaghi,et al.  On the estimation of the extreme value and normal distribution parameters based on progressive type-II hybrid-censored data , 2016 .

[5]  Hon Keung Tony Ng,et al.  Statistical Inference of Type-II Progressively Hybrid Censored Data with Weibull Lifetimes , 2009 .

[6]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[7]  Gordon Johnston,et al.  Statistical Models and Methods for Lifetime Data , 2003, Technometrics.

[8]  Abdus S. Wahed,et al.  BAYESIAN INFERENCE USING BURR MODEL UNDER ASYMMETRIC LOSS FUNCTION: AN APPLICATION TO CARCINOMA SURVIVAL DATA , 2008 .

[9]  Y. Tripathi,et al.  Estimating the parameters of a Burr distribution under progressive type II censoring , 2012 .

[10]  Narayanaswamy Balakrishnan,et al.  The Art of Progressive Censoring: Applications to Reliability and Quality , 2014 .

[11]  Ming-Hui Chen,et al.  Monte Carlo Estimation of Bayesian Credible and HPD Intervals , 1999 .

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

[13]  A. Papadopoulos.  The Burr Distribution as a Failure Model from a Bayesian Approach , 1978, IEEE Transactions on Reliability.

[14]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[15]  D. Lindley,et al.  Approximate Bayesian methods , 1980 .

[16]  Debasis Kundu,et al.  Hybrid censoring: Models, inferential results and applications , 2013, Comput. Stat. Data Anal..

[17]  Y. Tripathi,et al.  Inference on unknown parameters of a Burr distribution under hybrid censoring , 2013 .

[18]  Arezou Habibi Rad,et al.  Inference for Weibull distribution based on progressively Type-II hybrid censored data , 2011 .

[19]  Z. F. Jaheen,et al.  Statistical inference for the Burr model based on progressively censored data , 2002 .

[20]  A. Asgharzadeh,et al.  Estimation Based on Progressively Censored Data from the Burr Model , 2008 .

[21]  I. W. Burr.  Cumulative Frequency Functions , 1942 .

[22]  T. Louis.  Finding the Observed Information Matrix When Using the EM Algorithm , 1982 .

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

[24]  Chien-Tai Lin,et al.  Inference for the Weibull distribution with progressive hybrid censoring , 2012, Comput. Stat. Data Anal..

[25]  Debasis Kundu,et al.  Analysis of Type-II progressively hybrid censored data , 2006, Comput. Stat. Data Anal..