Weighted Least Squares Estimation of Location and Scale Parameters

SYNOPTIC ABSTRACT

The method of weighted least squares is used to estimate the location and scale parameters of distribution functions of the form F{(x-μ)/σ}. Explicit solutions are obtained for the parameter estimates and their variances. Applications are made to extreme value and normal distributions. A Monte Carlo study indicates the estimators are very good for means and good for variances.

Key Words and Phrases:

• Location and scale parameters
• weighted least squares estimation
• quantile function
• extreme value distribution
• normal distribution