Method of Moments: Weibull Distribution - Real Statistics We can estimate the mean μ and standard deviation σ of the population from the data in Figure 1. As we saw in Weibull Distribution, once we do this, we can estimate the scale and shape parameters based on the fact that. Estimating μ by x̄ and σ by s, it then follows that. Using algebra, we can now eliminate α to obtain. From which it ...