Renewed empirical formulas of Weibull distribution parameters estimates

The empirical formulas proposed in the literature for estimating the parameters of a two-parameter Weibull distribution, obtained using the equations of the moment method, are considered. It is noted that the formulas used to estimate the shape parameter take the form of various types of dependences on the coefficient of variation of the distribution. By modeling the empirical formulas selected for analysis, a comparative analysis of their errors relative to accurate numerical solutions of the moment method equations was carried out. A renewed empirical formula for the shape parameter is proposed. An approach to estimating the scale parameter is proposed, in which the empirical formula of the latter is reduced to the product of the standard deviation of the distribution by a power function of the coefficient of variation with an exponent equal to – 1.027. The results of applying the updated empirical formulas to numerical data obtained by modeling a random sample from the Weibull distribution are presented. It is shown that the accuracy of the proposed empirical formulas is quite high.