A robust iterative algorithm for parameter estimation of the generalized gamma distribution

Abstract

This paper introduces a robust iterative algorithm to estimate the parameters of the generalized gamma (GG) distribution. The proposed algorithm loops on an interval Ip of the shape parameterp such that the log-likelihood function are simplified as a univariate objective function for eachp ∈ Ip, which can be evaluated efficiently. An iterative procedure is then designed to maximize the objective function, which keeps squeezing the interval of search using translated asymptotes and interpolation. The results of maximization form a set of local maxima. Therefore, the estimates derived from the maximum of these local maxima. Comprehensive validation of the algorithm is performed as well, showing the robustness as well as efficiency as we expected. Due to the employment of the specific interpolation, the algorithm determines the roots with precision level of 10-10 within four iterations, which is a rather well-pleasing performance. We also claim that the flexibility of the algorithm allows us to transplant the algorithm to a distributed platform for very large scale data processing. Further optimization is still open to be discussed.