Approximation to the Mean and Variance of the Estimators Related to Gamma Distribution

In this thesis, we study the gamma distribution because it has many

applications in life – testing, survival and reliability investigation that appear in

medical studies of chronic diseases and industrial life – testing. Approximation to

the mean and variance of moments method estimators is made theoretically by

using Taylor series expansion approximated up to second partial derivatives. The

maximum likelihood estimators are derived and compared with several estimators

that proposed in the literature. Where the practice show that the bias values of

moment method estimators are adequate with the simulated bias values for

moderate and large sample. While the variance values of the scale parameter are

excellent in comparison with the simulated values.

A new bias corrected estimator based on the maximum likelihood estimator

is suggested and show better performance in comparison with the other estimators

proposed by McCullagh ,Nelder, Cardeiro, and Pearson.

The theoretical results are tested by using Monte – Carlo simulation and 

compared by utilizing the measurement of mean square error

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