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


Yilmaz H., SAZAK H. S.

MATHEMATICS AND COMPUTERS IN SIMULATION, vol.98, pp.18-30, 2014 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 98
  • Publication Date: 2014
  • Doi Number: 10.1016/j.matcom.2013.12.001
  • Title of Journal : MATHEMATICS AND COMPUTERS IN SIMULATION
  • Page Numbers: pp.18-30
  • Keywords: Generalized gamma distribution, Method of moments, Double-looped maximum likelihood, Parameter estimation, Chi-square goodness of fit test, RELIABILITY, MODEL

Abstract

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. (C) 2013 IMACS. Published by Elsevier B.V. All rights reserved.