A study of two estimation approaches for parameters of Weibull distribution based on WPP

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

72 Scopus Citations
View graph of relations



Original languageEnglish
Pages (from-to)360-368
Journal / PublicationReliability Engineering and System Safety
Issue number3
Publication statusPublished - Mar 2007
Externally publishedYes


Least-squares estimation (LSE) based on Weibull probability plot (WPP) is the most basic method for estimating the Weibull parameters. The common procedure of this method is using the least-squares regression of Y on X, i.e. minimizing the sum of squares of the vertical residuals, to fit a straight line to the data points on WPP and then calculate the LS estimators. This method is known to be biased. In the existing literature the least-squares regression of X on Y, i.e. minimizing the sum of squares of the horizontal residuals, has been used by the Weibull researchers. This motivated us to carry out this comparison between the estimators of the two LS regression methods using intensive Monte Carlo simulations. Both complete and censored data are examined. Surprisingly, the result shows that LS Y on X performs better for small, complete samples, while the LS X on Y performs better in other cases in view of bias of the estimators. The two methods are also compared in terms of other model statistics. In general, when the shape parameter is less than one, LS Y on X provides a better model; otherwise, LS X on Y tends to be better. © 2006 Elsevier Ltd. All rights reserved.

Research Area(s)

  • Censored data, Least-squares estimation, Monte carlo simulation, Pivotal function, Weibull distribution, Weibull probability plot