Parameter Estimation Through Weighted Least-Squares Rank Regression with Specific Reference to the Weibull and Gumbel Distributions

Author： van Zyl J. Martin Schall Robert

Publisher： Taylor & Francis Ltd

ISSN： 0361-0918

Source： Communications in Statistics: Simulation and Computation, Vol.41, Iss.9, 2012-10, pp. : 1654-1666

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

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.