PARAMETER ESTIMATION AND CONFIDENCE LIMIT CALCULATION METHOD OF THREE-PARAMETER WEIBULL DISTRIBUTION

Abstract

A correlation-regression method was proposed to solve the problem of low accuracy of parameter estimation and confidence limit calculation of the three-parameter Weibull distribution.The method was combined by the correlation coefficient method(Fu method)and the nonlinear regression method which makes full use of the convenience of Fu method and the excellent estimation effect of the nonlinear regression method in estimating the three-parameter Weibull distribution.In order to verify the effectiveness of the proposed method,the correlation-regression method,Fu method and the method combining maximum likelihood estimation and empirical formulae(referred to as the“MMPDS method”)were applied to the parameter estimation and confidence limit calculation of the data distribution of a certain alloy strength value with different sample sizes,and calculation consequence of different methods was compared and analyzed.Results show that the correlation-regression method has higher parameter estimation and confidence limit calculation accuracy among the above methods.When the sample size is less than 100,its advantage is more significant,and it can accurately calculate the parameters and confidence limits of the Weibull distribution.

Keywords

• Weibull distribution
• Parameter estimation
• Confidence limit