| In the dissertation, we derive the explicit expressions and some recurrence relations for the single and product moments of dual generalized order statistics from Burr Type III distribution and obtain characterizations of Burr Type III distribution using a recurrence relation for the moments and the conditional expectation of dual generalized order statistics. These results include the relations for the moments of reversed order statistics and lower record values as special cases. Luckily, the exact expression of the expected Fisher Information matrix of the parameters in the distribution is obtained. For the estimation of the parameters of Burr type III distribution based on dual generalized order statistics, two different approaches are considered, which are the maximum likelihood (ML) approach as well as the Bayesian approach. Also, an approximation based on Lindley is used to obtain the Bayes estimator. To compare the maximum likelihood estimator and the Bayes estimator of the parameters, Monte Carlo simulation study is performed. Moreover, MCMC method is used for the simulation study. Wingo (1983) introduced a clinical trial data about relief times for 50 patients with arthritis. The analysis for the real data set is included. |
