Bayesian and maximum likelihood estimations of the Dagum parameters under combined-unified hybrid censoring.

Abstract

In this paper, we introduce a new form of hybrid censoring sample, that is called COMBINED-UNIFIED (C-U) hybrid sample. In this unified approach, we merge the combined hybrid censoring sampling that considered by Huang and Yang [1] and unified hybrid censoring sampling that considered by Balakrishnan et al. [2]. We apply the C-U hybrid censoring sampling to develop estimation procedures of the unknown parameters of Dagum distribution. The maximum likelihood method is used to estimate the unknown parameters and the asymptotic confidence intervals as well as the bootstrap confidence intervals are obtained. Also, we develop the Bayesian estimation of the unknown parameters of Dagum distribution under the squared error and linear-exponential (LINEX) loss functions. Since the closed forms of the Bayesian estimators are not available, so we encounter some computational difficulties to evaluate the Bayes estimates of the parameters involved in the model such as Tierney and Kadanes procedure as well as Markov Chain Monte Carlo (MCMC) procedure to compute approximate Bayes estimates. In addition, we show the usefulness of the theoretical findings thought some simulation experiments. Finally, a real data set have been analyzed for illustrative purposes of our results.