  Estimation for the log-logistic and Weibull distributions can be performed by
using the equations used for probability plotting. The equations leads to
highly heteroscedastic regression. Exact expressions for the variances of the
residuals are derived which can be used to perform weighted regression. In
large samples maximum likelihood performs best, but it is shown that in smaller
samples the weighted regression outperforms maximum likelihood estimation with
respect to bias and mean square error.
