In this paper, the exponentiated generalized general class of distributions is introduced. Bayes estimators for the parameters, reliability and hazard rate functions are derived based on dual generalized order statistics. As a special model from exponentiated generalized general class distributions, Bayesian estimation for the unknown parameters, reliability and hazard rate functions of exponentiated generalized xgamma distribution based on dual generalized order statistics are considered. All results are specialized to lower records, also a numerical study is given to illustrate the theoretical procedures.