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Estimating the four parameters of the Burr III distribution using a hybrid method of variable neighborhood search and iterated local search algorithms

Zoraghi, N ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. DOI: 10.1016/j.amc.2012.03.003
  3. Publisher: 2012
  4. Abstract:
  5. The Burr III distribution properly approximates many familiar distributions such as Normal, Lognormal, Gamma, Weibull, and Exponential distributions. It plays an important role in reliability engineering, statistical quality control, and risk analysis models. The Burr III distribution has four parameters known as location, scale, and two shape parameters. The estimation process of these parameters is controversial. Although the maximum likelihood estimation (MLE) is understood as a straightforward method in parameters estimation, using MLE to estimate the Burr III parameters leads to maximize a complicated function with four unknown variables, where using a conventional optimization such as the gradient method is difficult. In this paper to circumvent the difficulty of maximizing the Burr III likelihood function, a meta-heuristics hybrid approach is proposed which composes of a variable neighborhood search (VNS) along with an iterated local search (ILS) algorithm. In the proposed algorithm, different heuristic local search methods are investigated to promote the ILS algorithm performance. Furthermore, the Taguchi technique is employed to tune the parameters. The results of some numerical examples and a simulation study indicate satisfactory performance of the proposed algorithm
  6. Keywords:
  7. Burr III distribution ; Iterated local search ; Maximum likelihood estimation ; Variable neighborhood search ; Algorithm performance ; Analysis models ; Complicated functions ; Conventional optimization ; Estimation process ; Exponential distributions ; Heuristic local search ; Hybrid approach ; Hybrid method ; Likelihood functions ; Log-normal ; Meta heuristics ; Numerical example ; Parameters estimation ; Reliability engineering ; Shape parameters ; Simulation studies ; Statistical quality control ; Straight-forward method ; Taguchi technique ; Weibull ; Algorithms ; Estimation ; Gradient methods ; Heuristic methods ; Models ; Weibull distribution ; Parameter estimation
  8. Source: Applied Mathematics and Computation ; Volume 218, Issue 19 , 2012 , Pages 9664-9675 ; 00963003 (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S0096300312002342