Research On Estimation For The Three-parameter Weibull Distribution

Weibull distribution has been widely used in reliability field, especially, the three-parameter Weibull distribution has the best goodness of fit for all kinds of life data. However, compared with the normal distribution or the exponential distribution, three-parameter Weibull distribution has more complicated structure and more unknown parameters, which restrict its application so far when sample size is small. This paper integrate the grey model and maximum likelihood method to propose a new method—grey-maximum likelihood method, which has excellent performances when sample size is small and works better for large sample size as well. Numerical simulations show that we can obtain proper estimate of the location parameter through grey-model method on small sample size condition, then we can transfer the problem into the estimation for the two-parameter Weibull distribution. Finally, we compare this modified method and traditional methods on different sample size condition by random simulation experiments, test of goodness of fit and probability plot, which illustrate the advantage of this method and show that the proposed method prevails over other methods especially in small sample size case.