Linear Regression Method for Binary Life Data from Weibull Distribution

Abstract

In order to solve the parameter estimate problem of Weibull distribution for binary life data without the maximum likelihood method, a linear regression method is given in this paper. By using the mean and variance formulas of interval statistic, the linear regression equation of two-parameter Weibull distribution for binary life data is established, the point estimate of regression equation parameters, the point estimate and the confidence limits of percentile and percentage of two-parameter Weibull distribution are also obtained. At last, an example is given in this paper. The point estimate of regression equation parameters is proved to be the best linear unbiased estimate according to Gauss-Markov theorem, so the property of the estimators is much better than the property of the estimators given by the maximum likelihood method, and the method in this paper is simpler and more convenient than the maximum likelihood method in the engineering.