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

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.

کلیدواژه ها:

Adaptive Type-II progressive censored samples ، Approximate maximum likelihood estimation ، Markov chain Monte Carlo algorithm ، Modified Weibull distribution