In this paper, the maximum liklihood estimation, unbiased estimations with minimum variance, percentile estimation, best percentile estimation single-observation estimation and the best percentile estimation two-observations in class which are based on order statistics are calculated in two sections for probability density and cumulative distribution functions of the beta Weibull geometric distribution, specially with bathtub-shaped and unimodal failure rate which are useful for modeling of data related to reliability and lifetime. Furthermore, through the simulation method of Monte Carlo and calculation of average square of errors of estimators, they are subjected to comparisons ultimately, the desirable estimator in each section is determined.