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Parameter Estimation Through Weighted Least-Squares Rank Regression with Specific Reference to the Weibull and Gumbel Distributions
Authors:J Martin van Zyl  Robert Schall
Institution:1. Department of Mathematical Statistics and Actuarial Science , University of the Free State , Bloemfontein , South Africa wwjvz@ufs.ac.za;3. Department of Mathematical Statistics and Actuarial Science , University of the Free State , Bloemfontein , South Africa
Abstract:Probability plots are often used to estimate the parameters of distributions. Using large sample properties of the empirical distribution function and order statistics, weights to stabilize the variance in order to perform weighted least squares regression are derived. Weighted least squares regression is then applied to the estimation of the parameters of the Weibull, and the Gumbel distribution. The weights are independent of the parameters of the distributions considered. Monte Carlo simulation shows that the weighted least-squares estimators outperform the usual least-squares estimators totally, especially in small samples.
Keywords:Estimation  Gumbel distribution  Probability plot  Rank regression  Weibull distribution  Weighted least-squares regression
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