Double-looped maximum likelihood estimation for the parameters of the generalized gamma distribution

The generalized gamma distribution (GGD) is a very popular distribution since it includes many well known distributions. Estimation of the parameters of the GGD is quite problematic because of the complicated structure of its density function. We introduce two new estimation methods called maximum likelihood with goodness of fit test (MLGOFT) and double-looped maximum likelihood (ML) estimation. We show through simulations under several situations that the MLGOFT method is more efficient than the Method of Moments with goodness of fit test (MMGOFT) technique especially for small and moderate sample sizes whereas the double-looped ML is the superior estimation method for all cases. The double-looped ML method is also very fast, practical and straightforward.