The method of three-parameter Weibull distribution estimation

Abstract. In this paper we develop Maximum Likelihood (ML) and Improved Analytical (IA) numerical algorithms to estimate parameters of the Weibull distribution, namely, location, scale and shape parameters, using order statistics of a noncensored sample. Since ML method leads to multiextremal numerical problem we establish conditions to localize extremes of the ML function, which enables us to avoid problems related with ML estimation failure and to create a simple estimation procedure by solving one-dimensional equation. IA estimation also has been developed by solving the equation in one variable. The estimates proposed are studied by computer modeling and compared with the theoretical ones with respect to sample size and number of order statistics used for estimation. Recommendations for implementation of the estimates are also discussed.