The pitman estimator of the gamma scale parameter and comparing it with some estimation methods

الملخص EN

The research studied the Pitman Estimation Method for estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter for for for for the two parameter Gamma Distribution, and compared it with some estimation methods for estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter estimation the scale parameter .

The methods are: Maximum likelihood Estimator Method (MLE), Standard Bayesian Method (SB), Furthermore; the researcher suggested two mixture methods for estimation; the first Mixture Method between Maximum Likelihood Estimator Method and Pitman Method (MIX I), and the second Mixture Method between Standard Bayesian Method and Pitman Method (MIX II).

Comparison was conducted between the methods mentioned above to estimate the scale parameter in the experimental aspect to find the best estimation method.

Generally, a comparison between the estimation methods of estimating the scale parameter is made using the relative efficiency of the risk efficiency under squared error loss function to find the best method through Monte Carlo simulation.

Simulation examples are worked out, where the generation of random data, depending on the different sample sizes and run size (L=1000).

The Pitman method is found to be the best method for estimation the scale parameter.