Estimation of Parameters and Reliability Characteristics in Lindley Distribution Using Randomly Censored Data
AbstractThis article deals with the estimation of parameters and reliability characteristics of Lindley distribution underrandom censoring. Expected time on test based on randomly censored data is obtained. The maximum likelihood estimators of the unknown parameters and reliability characteristics are derived. The asymptotic, bootstrap p and bootstrap t confidence intervals of the parameters are constructed. The Bayes estimators of the parameters and reliability characteristics under squared error loss function using non-informative and gamma informative priors are obtained. For computing of Bayes estimates, Lindley approximation and MCMC methods are considered. Highest posterior density (HPD) credible intervals of the parameters are obtained using MCMC method. Various estimation procedures are compared using a Monte Carlo simulation study. Finally, a real data set is analyzed for illustration purposes.
Akaike H (1974) A new look at the statistical models identification IEEE Trans. on Automatic Control, AC 19:716-723.
Ali S, Aslam M, Kazmi SMA (2013) A study of the effect of the loss function on Bayes estimate, posterior risk and hazard function for Lindley distribution Appl Mathe Model 37:6068-6078.
Breslow N, Crowley J (1974) A large sample study of the life table and product limit estimates under random censorship Ann of Stat 2:437-453.
Chen MH, Shao QM (1999) Monte Carlo estimation of Bayesian credible and HPD intervals. J of Comput Graph Stat 8:69–92.
Danish MY, Aslam M (2013) Bayesian estimation for randomly censored generalized exponential distribution under asymmetric loss functions J of Appl Stat 40 (5):1106-1119.
Danish MY, Aslam M (2014) Bayesian inference for the randomly censored Weibull distribution J of Stat Comput Simul 84(1):215-230.
Dube M, Garg R, Krishna H (2016) On progressively first failure censored Lindley distribution Comput Stat 31(1):139-163.
Efron B, Tibshirani RJ (1993) An introduction to the Bootstrap. New York: Chapman and Hall.
Efron B (1982) The Jacknife, the bootstrap and other re-sampling plans, CBMS-NSF Regional Conference Series in Applied Mathematics Society, SIAM 38.
Efron B (1967) The two sample with censored data. Proc. Fifth Berkeley Symp. Math. Statisti. Prob. 4: 831-853.
Fleming TR, Harrington DP (1991) Counting Processes and Survival Analysis. New York: Wiley.
Garg R, Dube M, Kumar K, Krishna H (2016) On randomly censored generalized inverted exponential distribution Ameri J of Mathe Manag Scien 35(4):361-379.
Ghitany ME, Atieh B, Nadarajah S (2008) Lindley distribution and its applications Mathe Comput in Simul 78:493-506.
Gilbert JP (1962) Random censorship. Ph.D. thesis, University of Chicago.
Gupta PK, Singh B (2013) Parameter estimation of Lindley distribution with hybrid censored data Int J of Sys Assu Eng Manag 4(4):378–385.
Hall P (1988) Theoretical comparison of bootstrap confidence intervals Ann of Stat 16:327–953.
Kaplan EL, Meier P (1958) Nonparametric estimation from incomplete observations J of Ameri Stati Assoc 53:457-481.
Kim N (2014) Approximate MLE for the scale parameter of generalized exponential distribution under random censoring. J of the Korea Stat Socie 43:119-131.
Klein JP, Moeschberger ML (1997) Survival Analysis: Techniques for Censored and Truncated Data. New York: Springer-Verlag.
Krishna H, Kumar K (2011) Reliability estimation in Lindley distribution with progressively type II right censored sample Mathe Compu in Simul 82:281-294.
Krishna H, Vivekanand, and Kumar K (2015) Estimation in Maxwell distribution with randomly censored data J of Stat Comput and Simul. 85(17):3560-3578.
Kumar K, Krishna H, Garg R (2015) Estimation of P(Y < X) in Lindley distribution using progressively first failure censoring Int J of Syst Assur Eng Manag 6(3):330-341.
Lawless JF (2003) Statistical Models and Methods for Lifetime Data, 2nd ed. New York: Wiley.
Lindley DV (1980) Approximate Bayes methods. Trabajos de Estadistica. 31:223–237.
Lindley DV (1958) Fiducial distributions and Bayes’ theorem. J of Royal Stat Society, Series B. 20:102-107.
Mazucheli J, Achcar JA (2011) The Lindley distribution applied to competing risks lifetime data Comput Methods Progr Biomed 104:188-192.
Ntzoufras I (2009) Bayesian Modeling Using WinBugs. New York: Wiley.
Saleem M, Raza A (2011) On Bayesian Analysis of the exponential survival time assuming the exponential censor time Pak J of Sci 63(1):44-48.
Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6(2):421–464.
Zheng G., Gastwirth J.L (2001) On the Fisher information in randomly censored data Stat and Prob Lett 52:421-426.
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).