In this paper, compared eight methods for generating the initial value and the impact of these methods to estimate the parameter of a autoregressive model, as was the use of three of the most popular methods to estimate the model and the most commonly used by researchers MLL method, Barg method  and the least squares method and that using the method of simulation model  first order autoregressive through the design of a number of simulation experiments and the different sizes of the samples.

Background:  Ultrasound provides a powerful tool for assessing early pregnancy and detecting pregnancy failure at first trimester and promoting rapid effective management. Several  criteria have been established  to predict  the pregnancy outcome particularly in symptomatic women .

Aim: To evaluate  asymptomatic women at the first trimester of pregnancy , to assess the efficacy of certain ratios as mid sac diameter (MSD)  / yolk sac ratio & crown rump length (CRL)/mid sac diameter (as indicator  of early first trimester oligohydramnios)  in predicting poor 1^st   trimester outcome

Type of the study: A cross-s

In this research the Empirical Bayes method is used to Estimate the affiliation parameter in the clinical trials and then we compare this with the Moment Estimates for this parameter using Monte Carlo stimulation , we assumed that the distribution of the observation is binomial distribution while the distribution with the unknown random parameters is beta distribution ,finally we conclude that the Empirical bayes method for the random affiliation parameter is efficient using Mean Squares Error (MSE) and for different Sample size .