The exponentiated gamma distribution is a two parameters lifetime distribution with monotone and non-monotone failure rates. In this article, some estimation methods of the probability density function and the cumulative distribution function of the exponentiated gamma distribution such as uniformly minimum variance unbiased (UMVU), maximum likelihood (ML), least squares, weighted least squares and Minimum distance estimators are studied and their performances through numerical simulations are compared. By the mean integrated squared error (MISE), the UMVU and ML are approximately equivalent and more efficient than the others based on simulation studies when the sample size is more than 40. A real data set is analyzed for illustrative purposes.
