From Zhentong Gao Method to Generalized Zhentong Gao Method

Abstract

It is found that the data of structural fatigue life are mostly in accordance with Weibull distribution rather than Gaussian distribution, but the biggest obstacle affecting the application of Weibull distribution is that the estimation of its three- parameters will encounter difficulties in mathematical derivation and complicated calculation. Based on the estimation of correlation coefficient, the author has proposed Zhentong Gao method (Z.T. Gao method) which can avoid these difficulties. Further research found that the idea of Z.T. Gao method can be used to directly calculate the maximum value of the likelihood function of three-parameter Weibull distribution and estimate the three parameters simultaneously, which is called Generalized Zhentong Gao method. At the same time, it is also found that Nonlinear Programming method and Boltzmann Annealing method in machine learning can estimate the three parameters of Weibull distribution by directly calculating the maximum of likelihood function, so they can be regarded as Generalized Z. T. Gao methods in a sense. The results obtained by these methods are compared and some enlightening conclusions are obtained.