Parameter Estimations in a Bernoulli Process

In this paper, we study the parameter estimation in Bernoulli distribution and Geometric distribution with parameter . We consider the estimator of and we find two confidence intervals for the parameters in these distributions. One is the result of variance stabilization(V. S.) and the other is that of using central limit theorem(C. L. T.). Simulation results shows that the point estimates are not so different and the length of the confidence intervals obtained by V. S. in case of geometric distribution is smaller than that by C. L. T.