Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

BAYESIAN AND CLASSICAL INFERENCE FOR TOPP-LEONE INVERSE WEIBULL DISTRIBUTION BASED ON TYPE-II CENSORED DATA

  • ZAHRA SHOKOOH GHAZANI (Department of Statistics and Mathematics, Central Tehran Branch, Islamic Azad University)
  • Received : 2023.09.19
  • Accepted : 2024.05.29
  • Published : 2024.07.30
Download PDF
⟨ Previous Next ⟩

Abstract

This paper delves into an examination of both non-Bayesian and Bayesian estimation techniques for determining the Topp-leone inverse Weibull distribution parameters based on progressive Type-II censoring. The first approach employs expectation maximization (EM) algorithms to derive maximum likelihood estimates for these variables. Subsequently, Bayesian estimators are obtained by utilizing symmetric and asymmetric loss functions such as Squared error and Linex loss functions. The Markov chain Monte Carlo method is invoked to obtain these Bayesian estimates, solidifying their reliability in this framework.

Keywords

Acknowledgement

The author is thankful to the referees for the useful suggestions.

References

  1. B. Epstein, Estimation truncated life-tests in the exponential case, Ann. Math. Stat. 25 (1954), 555-564.  https://doi.org/10.1214/aoms/1177728723
  2. D.R. Cox and D. Oakes, Analysis of Survival Data, Chapman and Hall, New York, 1984. 
  3. M. Crowder, A. Kimber, R. Smith, and T. Sweeting, Statistical Analysis of Reliability Data, Chapman and Hall, London, 1991. 
  4. J.F. Lawless, Statistical Models and Methods for Lifetime Data, Wiley, New York, 2003. 
  5. K.S. Sultan, N.H. Alsadat and D. Kundu, Bayesian and Maximum Likelihood Estimations of the Inverse Weibull Parameters under Progressive type-II Censoring, Journal of Statistical Computation and Simulation 84 (2014), 2248-2265.  https://doi.org/10.1080/00949655.2013.788652
  6. S.K. Singh, U. Singh, M. Kumar and P.K. Vishwakarma, Classical and Bayesian Inference for an Extension of the Exponential Distribution under Progressive Type-II Censored Data with Binomial Removals, Journal of Statistics Applications & Probability 1 (2014), 75-86.  https://doi.org/10.12785/jsapl/010304
  7. D. Kumar, U. Singh, S.K. Singh and G. Bhattacharyya, Bayesian Estimation of Exponentiated Gamma Parameter for Progressive Type II Censored Data With Binomial Removals, Journal of Statistics Applications & Probability 4 (2015), 265-273. 
  8. M. Kumar, S.K. Singh and U. Singh, Bayesian Inference for Poisson-Inverse Exponential Distribution under Progressive Type-II Censoring with Binomial Removal, International Journal of System Assurance Engineering and Management 9 (2018), 1235-1249. 
  9. A. Pathak, M. Kumar, S.K. Singh and U. Singh, Bayesian Inference: Weibull Poisson Model for Censored Data Using the Expectation-Maximization Algorithm and its Application to Bladder Cancer Data, Journal of Applied Statistics 49 (2022), 926-948.  https://doi.org/10.1080/02664763.2020.1845626
  10. R.J.A. Little and D.B. Rubin, Incomplete Data, In Encyclopedia of Statistical Sciences, (Eds S. Kotz and N. L. Johnson), Wiley, New York, 1983. 
  11. A.P. Dempster, N.M. Laird and D.B. Rubin, Maximum Likelihood from Incomplete Data via the EM Algorithm, Journal of the Royal Statistical Society: Series B (Methodological) 39 (1977), 1-22.  https://doi.org/10.1111/j.2517-6161.1977.tb01600.x
  12. E. Moradi and Z. Shokooh Ghazani, A Novel Weibull Marshall- Olkin Power Lomax Distribution: Properties and Applications to Medicine and Engineering, Journal of Applied Mathematics and Informatics 41 (2023), 1275-1301.  https://doi.org/10.14317/JAMI.2023.1275
  13. Z.S. Ghazani, Symmetrization procedures for the law of the iterated logarithm, Journal of Mathematical Analysis 12 (2021), 44-53. 
  14. L. Tierney, Markov Chains for Exploring Posterior Distributions, The Annals of Statistics 24 (1994), 1701-1728. 
  15. Z. Shokooh Ghazani, Shrinkage Estimators for shape parameter of Gompertz Distribution, Journal of Statistical Theory and Practice 18 (2024).