Formulas to describe the bias and standard deviation of the ML-estimated Weibull shape parameter

The purpose of this paper is to present two formulas which can be used with the maximum likelihood method to estimate the Weibull shape parameter from uncensored data. The first formula unbiases the shape parameters for sample sizes of 3 and up. If this formula is added to the standard ML method, the bias is reduced to typically <0.3% (or even <0.05% depending on which set of test data is chosen) of the shape parameter value. The second formula gives the relative standard deviation of the shape parameter estimator with an error of typically <1%. Both formulas are derived from an assumed relationship between the sample size and the asymptotic behavior of a parameter under consideration. In addition, an unbiasing formula is given for the generalized ML method