Mathematical Researches

Historically, various methods were suggested for the estimation of Bernoulli and Binomial distributions parameter. One of the suggested methods is the Bayesian method, which is based on employing prior distribution. Their sound selection on parameter space play a crucial role in reducing posterior Bayesian estimator error. At times, large scale of the parametric changes on parameter space brings about an increase in error rate and enlargement of the comparison criteria .therefore, determining appropriate prior distribution on parameter space plays a key part in reducing comparison criteria. Accordingly, in this paper appropriately modified prior distribution was considered for Binomial distribution parameter and then, while extending certain conditions on  prior distribution hyperparameters, an effective estimate under the title Expected Bayesian Estimate  (AKA E-Bayes) would  be proposed. At last, to evaluate the measurement  methodologies  utilized in this paper, under MSE criteria , extensive simulation studies were conducted, and the results were analyzed and above mentioned methods will be applied in a real example.