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

• Published in: Reliability engineering & system safety Vol. 92; no. 3; pp. 360 - 368
• Main Authors: Zhang, L.F., Xie, M., Tang, L.C.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Oxford Elsevier Ltd 01-03-2007; Elsevier
• Subjects: Applied sciences; Censored data; Exact sciences and technology; Least-squares estimation; Monte carlo simulation; Operational research and scientific management; Operational research. Management science; Pivotal function; Reliability theory. Replacement problems; Weibull distribution; Weibull probability plot; Censored data; Least-squares estimation; Monte carlo simulation; Weibull distribution; Pivotal function; Weibull probability plot; Monte Carlo method; Parameter estimation; Statistical analysis; Probabilistic approach; Bias; Complete sample; Censored sample; Modeling; Least squares method; Observer; Small sample; System identification; Biased estimation
• ISSN: 0951-8320; 1879-0836
• DOI: 10.1016/j.ress.2006.04.008

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.