Novel algorithm for reconstruction of a distribution by fitting its first-four statistical moments

Abstract This paper proposes a novel algorithm to reconstruct an unknown distribution by fitting its first-four moments to a proper parametrized probability distribution (PPD) model. First, a PPD system containing three previously developed PPD models is suggested to approximate the unknown distribution, rather than empirically adopting a single distribution model. Then, a two-step algorithm based on the moments matching criterion and the maximum entropy principle is proposed to specify the appropriate (final) PPD model in the system for the distribution. The proposed algorithm is first verified by approximating several commonly used analytical distributions, along with a set of real dataset, where the existing measures are also employed to demonstrate the effectiveness of the proposed two-step algorithm. Further, the effectiveness of the algorithm is demonstrated through an application to three typical moments-based reliability problems. It is found that the proposed algorithm is a robust tool for selecting an appropriate PPD model in the system for recovering an unknown distribution by fitting its first-four moments.

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