TARU PUBLICATIONS
Journal of Statistics and Management Systems cover

Journal of Statistics and Management Systems

(Since 1998)
Hybrid ·Peer-reviewed·ISSN (Online): 2169-0014·ISSN (Print): 0972-0510

Indexed in ABDC Australia

Powered by:Powered by

Monthly Journal: Publishes peer-reviewed aticles on theoretical and applied statistics and management systems, expoloring industrial statistics, actuarial and decision sciences.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Taru Online First Current IssueSpecial IssuesBrowse all Issues
Journal of Statistics and Management Systems
Open Access Research Article

Using Bayesian and classical methods to estimation parameter for inverse Pareto distribution under randomly censored data

, *

* Corresponding author · click or hover a name for details

pp. 971–983Vol. 27Issue 5July 2024DOI: 10.47974/JSMS-1273XML
Received:
09 Jan 2024
Published Online:
05 Aug 2024
Article type:
Research Article
Language:
EN
Article no.:
JSMS-1273
Pages:
971–983

Abstract

In this article, we will use randomly censored data and to discuss both Bayesian and classical methods to the estimating parameters the inverse Pareto distribution (IPD). We derive the Bayes and maximum likelihood methods to obtain the parameters estimators. Asymptotic confidence intervals for the parameters are computed by using the observed Fisher information matrix. Using gamma informative priors, Bayes estimators for the parameters are derived under the (LINEX) loss function. For Bayesian estimates, the method of Markov Chain Monte Carlo (MCMC) is employed. In addition, using (MCMC) techniques, credible intervals with the largest posterior density for the parameters are generated. A simulation study compares how well each estimators performs. Lastly, two real datasets are taken into consideration for demonstration.

Keywords

Bayesian estimationRandom censoringMarkov Chain Monte Carlo TechniquesAsymptotic confidence interval(HPD) credible intervalMaximum likelihood estimation

Subject Classifications

11J7111K06

References

[1] Akaike, H.  A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716-723 (1974).
[2] Breslow, N. and J. Crowley. A large sample study of the life table and product limit estimates under random censorship. The Annals of Statistics, 2(3), 437-453. Chaturvedi, A., N (1974). 
[3] Kumar and K. Kumar. Statistical inference for the reliability functions of a family of lifetime distributions based on progressive type II right censoring. Statistical, 78(1), 81-101 (2018).  
[4] Chen, M.H. and Q. Shao. Monte Carlo estimation of Bayesian credible and HPD intervals. Journal of Computational and Graphical Statistics, 8(1), 69-92 (1999). 
[5] Garg, Renu, D. Madhulika and H. Krishna. Estimation of parameters and reliability characteristics in Lindley distribution using randomly censored data. To appear in Statistics, Optimization and Information (2019). 
[6] Garg, R., M. Dube, K.Kumar and H. Krishna. On randomly censored generalized inverted exponential distribution. American Journal of Mathematical and Management Sciences, 35(4), 361-379 (2016).
[7]  Ghitany, M. and S. Al-Awadhi. Maximum likelihood estimation of Burr XII distribution parameters under random censoring. J. Applied Statistics, 29(7), 955-965 (2002). 
[8] Gilbert, J.P. Random Censorship. Ph.D Thesis, University of Chicago, Department of Statistics (1962). 
[9] Hastings, W.K. Monte Carlo sampling methods using Markov chains and their applications. 57, 97-109 (1970).
[10]  Koziol, J.A. and S.B. Green. A Cram–er-Von Mises statistic for randomly censored data. Biometrika, 63(3), 465-474 (1976). 
[11] Krishna, H. and N. Goel. Randomly censored geometric distribution under Koziol-Green model. Int. J. Agricult. Stat. Sci., 13(1), 85-95 (2017).
[12] Krishna, H. and K. Kumar. Reliability estimation in generalized gamma distribution with progressively censored data. Int. J. Agricult. Stat (2017).  
[13] Krishna, H. and K. Kumar. Reliability estimation in generalized inverted exponential distribution with progressively type II censored sample. J. Statistical Computation and Simulation, 83(6), 1007-1019 (2013). 
[14] Krishna, H., Vivekanand and K. Kumar. Estimation in Maxwell distribution with randomly censored data. J. Statistical Computation and Simulation, 85(17), 3560- 3578 (2015). 
[15] Kumar, K. Classical and Bayesian estimation in loglogistic distribution under random censoring. International Journal of System Assurance Engineering and Management, 9(2), 440-451 (2018).
[16]  Kumar, K. and R. Garg. Estimation of the parameters of randomly censored generalized inverted Rayleigh distribution. Sci., 10(1), 147-155 (2014).
[17] Kumar, K. R. Garg and H. Krishna. Nakagami distribution as a reliability model under progressive censoring. Int. J. System Assurance Engineering and Management, 8(1), 109-122 (2017).  
[18] Kumar, K. and I. Kumar. Estimation in inverse Weibull distribution based on randomly censored data. Statistica, 79(1), 47-74 (2019). 
[19] Lawless, J. F. Statistical Models and Methods for Lifetime Data. Floboken, New Jersey. Mann, N.R., N.D. (2003). 
[20] Singpurwalla and R.E. Schafer. Methods for Statistical Analysis of Reliability and Life Data. Wiley, New York (1974).  
[21] Metropolis, N., A.W. Rosenbluth, M.N. Rosenbluth, A. H. Teller and E. Teller. Equation of state calculations by fast computing machines. The Journal of Chemical Physics, 21(6), 1087-1092 (1953). 
[22] Ntzoufras, I. Bayesian Modeling Using WinBugs. Wiley, New (2009). 
[23] R Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria (2018). 
[24] Robert, C. and G. Casella. Monte Carlo Statistical Methods. Verlag NY (2004). 
[25] Schwarz, G. Estimating the dimension of a model. The Annals of Statistics, 6(2), 461-464 (1978).
[26] Sinha, S.K. Reliability and Life Testing. Wiley Eastern Limited, New Delhi (1986). 
[27] Varian, H.R. A Bayesian approach to real estate assessment. Studies in Bayesian Econometric and Statistics in Honor of Leonard J. Savage Savage, eds. Stephen E. Fienberg and Arnold (1975) 
[28] Zellner, Amsterdam: North- Hollan. Zellner, A. Bayesian estimation and prediction using asymmetric loss functions. Journal of the American Statistical Association, 81(394), 446-451 (1986).

Views: 226Downloads: 69Citations: 0