Estimations of the parameters for modified Weibull distribution under adaptive type-II progressive censored samples

Document Type : Original Scientific Paper

Authors

Department of Statistics‎, ‎Imam Khomeini International University‎, ‎Qazvin‎, ‎Iran

Abstract

This paper describes the point and interval estimation of the unknown parameters of modified Weibull distribution under the adaptive Type-II progressive censored samples‎. ‎First‎, ‎we obtain the maximum likelihood estimation of parameters‎. ‎Because maximum likelihood estimations should be solved in numerical methods and cannot be derived in a closed form‎, ‎the approximate maximum likelihood estimations of the parameters are achieved‎. ‎Also‎, ‎asymptotic confidence intervals are obtained by earning the asymptotic distribution of the parameters‎. ‎Moreover‎, ‎two bootstrap confidence intervals are derived‎. ‎Second‎, ‎the Bayesian estimation of parameters is approximated using the Markov chain Monte Carlo algorithm and Lindley's method‎. ‎Furthermore‎, ‎the highest posterior density credible intervals of the parameters are derived‎. ‎Finally‎, ‎the different proposed estimations have been compared by the simulation studies and one data set is analyzed to illustrative aims.

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References

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Journal of Statistical Modelling: Theory and Applications
Volume 4, Issue 1
January 2023
Pages 75-93

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History

  • Receive Date: 26 June 2023
  • Revise Date: 12 March 2024
  • Accept Date: 31 March 2024

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