Inverted Topp-Leone Distribution: Contribution to a Family of J-Shaped Frequency Functions in Presence of Random Censoring
In this paper, Bayesian and non-Bayesian estimation of the inverted Topp-Leone distribution shape parameter are studied when the sample is complete and random censored. The maximum likelihood estimator (MLE) and Bayes estimator of the unknown parameter are proposed. The Bayes estimates (BEs) have been computed based on the squared error loss (SEL) function and using Markov Chain Monte Carlo (MCMC) techniques. The asymptotic, bootstrap (p,t), and highest posterior density intervals are computed. The Metropolis Hasting algorithm is proposed for Bayes estimates. Monte Carlo simulation is performed to compare the performances of the proposed methods and one real data set has been analyzed for illustrative purposes.
Topp, C.W. and Leone, F.C. (1955). A family of J-shaped frequency functions, Journal of the American Statistical Association, 50, 209–219.
Nadarajah, S. and Kotz, S. (2003). Moments of some J-shaped distributions, Journal of Applied Statistics, 30, 311–317.
Ghitany, M.E., Kotz, S. and Xie, M. (2005). On some reliability measures and their stochastic ordering for the Topp–Leone distribution, Journal of Applied Statistics, 32, 715–722.
Bayoud, H. (2016). Admissible minimax estimators for the shape parameter of Topp–Leone distribution, Communications in Statistics-Theory and Methods, doi: 10.1080/03610926.2013.818700.
Muhammed, H.Z. (2019). On The Inverted Topp-Leone Distribution, international journal of reliability and applications, 20, 17–28.
Dey, S., Singh, S., Tripathi, Y.M. and Asgharzadeh, A. (2016). Estimation and prediction for a progressively censored generalized inverted exponential distribution. Statistical Methodology, 132, 185–202.
Ravenzwaaij, D.V., Cassey, P. and Brown, S.D. (2018). A simple introduction to Markov Chain Monte-Carlo sampling. Psychonomic Bulletin Review, 25, 143–154.
Dey, S. and Pradhan, B. (2014). Generalized inverted exponential distribution under hybrid censoring. Statistical Methodology, 18, 101–114.
Efron, B., and Tibshirani, R. J. (1993). An Introduction to the Bootstrap. New York: Chapman and Hall.
Hall, P. (1988). Theoretical comparison of bootstrap confidence intervals. The Annals of Statistics, 927–953.
Lawless, J. F. (2011). Statistical Models And Methods for Lifetime Data, Second edition. John Wiley & Sons, Inc, Canada.
Kalbfleisch, J. D. and Prentice, R. L. (1980). The Statistical Analysis of Failure Time Data. New York: Wiley.