Inverted Topp-Leone Distribution: Contribution to a Family of J-Shaped Frequency Functions in Presence of Random Censoring

Authors

  • Hiba Zeyada Muhammed Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University, Egypt
  • Essam Abd Elsalam Muhammed Department of Management and Financial, High Institute of Computer and Information Technology, Elshorouk Academy, Egypt

DOI:

https://doi.org/10.13052/jrss0974-8024.14212

Keywords:

Inverted Topp leone distribution, moments, order statistic, maximum likelihood estimation, Bayesian estimation, MCMC, highest posterior density interval, asymptotic confidence interval, bootstrap confidence interval, random censoring

Abstract

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.

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Author Biographies

Hiba Zeyada Muhammed, Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University, Egypt

Hiba Zeyada Muhammed received a bachelor’s degree in Statistics from the Faculty of Science at Cairo University in 2006, a master’s degree in Statistics from Cairo University in 2009, and philosophy of doctorate in statistics from Cairo University in 2013, respectively. She is currently working as an Associative Professor at the Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University. Her research areas include Reliability, life testing, bivariate and multivariate analysis, copula modeling and ranked set sampling. She has been serving as a reviewer for many highly-respected journals.

Essam Abd Elsalam Muhammed, Department of Management and Financial, High Institute of Computer and Information Technology, Elshorouk Academy, Egypt

Essam Abd Elsalam Muhammed received a bachelor’s degree in applied Statistics from the Faculty of Commerce at kafr El-sheikh University in 2015, a master’s degree in Statistics from Cairo University in 2020, and in the preparatory year of the doctorate in statistics at Cairo University, respectively. He is currently working as a teaching assistant at High Institute of Computer and Information Technology, Elshorouk Academy. his research areas include Reliability and life testing.

References

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.

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Published

2021-12-06

How to Cite

Muhammed, H. Z. ., & Muhammed, E. A. E. . (2021). Inverted Topp-Leone Distribution: Contribution to a Family of J-Shaped Frequency Functions in Presence of Random Censoring. Journal of Reliability and Statistical Studies, 14(02), 615–650. https://doi.org/10.13052/jrss0974-8024.14212

Issue

2021: Vol 14 Iss 2

Section

Articles