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Estimation of G-renewal process parameters as an ill-posed inverse problem

Authors
Journal
Reliability Engineering & System Safety
0951-8320
Publisher
Elsevier
Volume
115
Identifiers
DOI: 10.1016/j.ress.2013.02.005
Keywords
  • G-Renewal Process
  • Underlying Distribution
  • Monte Carlo Simulation
  • Inverse Problems
  • Regularization
Disciplines
  • Mathematics

Abstract

Abstract Statistical estimation of G-renewal process parameters is an important estimation problem, which has been considered by many authors. We view this problem from the standpoint of a mathematically ill-posed, inverse problem (the solution is not unique and/or is sensitive to statistical error) and propose a regularization approach specifically suited to the G-renewal process. Regardless of the estimation method, the respective objective function usually involves parameters of the underlying life-time distribution and simultaneously the restoration parameter. In this paper, we propose to regularize the problem by decoupling the estimation of the aforementioned parameters. Using a simulation study, we show that the resulting estimation/extrapolation accuracy of the proposed method is considerably higher than that of the existing methods.

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