Abstract
ABSTRACT In this paper, we discuss computational aspects to obtain accurate inferences for the parameters of the generalized gamma (GG) distribution. Usually, the solution of the maximum likelihood estimators (MLE) for the GG distribution have no stable behavior depending on large sample sizes and good initial values to be used in the iterative numerical algorithms. From a Bayesian approach, this problem remains, but now related to the choice of prior distributions for the parameters of this model. We presented some exploratory techniques to obtain good initial values to be used in the iterative procedures and also to elicited appropriate informative priors. Finally, our proposed methodology is also considered for data sets in the presence of censorship.
Highlights
The Generalized gamma (GG) distribution is very flexible to be fitted by reliability data due to its different forms for the hazard function
The inferential procedures for the gamma distribution can be be obtained by classical and Bayesian approaches, especially using the computational advances of last years in terms of hardware and software [2], the inferential procedures for the generalized gamma distribution under the maximum likelihood estimates (MLEs) can be unstable (e.g., [8,14,24,25]) and its results may depend on the initial values of the parameters chosen in the iterative methods
An exploratory technique is discussed to obtain good initial values for numerical procedure used to obtain the MLEs for generalized gamma (GG) distribution parameters
Summary
The Generalized gamma (GG) distribution is very flexible to be fitted by reliability data due to its different forms for the hazard function. The inferential procedures for the gamma distribution can be be obtained by classical and Bayesian approaches, especially using the computational advances of last years in terms of hardware and software [2], the inferential procedures for the generalized gamma distribution under the maximum likelihood estimates (MLEs) can be unstable (e.g., [8,14,24,25]) and its results may depend on the initial values of the parameters chosen in the iterative methods. An intensive simulation study is presented in order to verify our proposed methodology These results are of great practical interest since it enable us for the use of the GG distribution in many application areas.
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