Abstract
The Weibull distribution plays a central role in modeling duration data. Its maximum likelihood estimator is very sensitive to outliers. We propose three robust and explicit Weibull parameter estimators: the quantile least squares, the repeated median and the median/Q n estimator. We derive their breakdown point, influence function, asymptotic variance and study their finite sample properties in a Monte Carlo study. The methods are illustrated on real lifetime data affected by a recording error.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adatia A, Chan L (1982) Robust procedures for estimating the scale parameter and predicting future order statistics of the Weibull distribution. IEEE Trans Reliab 31: 491–498
Cohen AC (1965) Maximum likelihood estimation in the Weibull distribution based on complete and on censored samples. Technometrics 7: 579–588
Dixit UJ (1994) Bayesian approach to prediction in the presence of outliers for Weibull distribution. Metrika 41: 127–136
Hampel FR, Ronchetti E, Rousseeuw PJ, Stahel W (1986) Robust statistics. The approach based on influence functions. Wiley, New York
Hampel FR (1974) The influence curve and its role in robust estimation. J Am Stat Assoc 69: 383–393
He X, Fung WK (1999) Method of medians for lifetime data with Weibull models. Stat Med 18: 1993–2009
Hoel D (1972) A representation of mortality data by competing risks. Biometrics 28: 475–488
Huber P (1981) Robust statistics. Wiley, New York
Kalbfleisch J, Prentice R (1980) The statistical analysis of failure time data. Wiley, New York
Li Y-M (1994) A general linear-regression analysis applied to the 3-parameter Weibull distribution. IEEE Trans Reliab 43: 255–263
Lingappaiah G (1976) Effect of outliers on the estimation of parameters. Metrika 23: 27–30
Marks N (2005) Estimation of Weibull parameters from common percentiles. J Appl Stat 32: 17–24
Muralidharan K, Lathika P (2006) Analysis of instantaneous and early failures in Weibull distribution. Metrika 64: 305–316
Olive D (2006) Robust estimators for transformed location scale families. Mimeo
Rousseeuw PJ, Croux C (1993) Alternatives to the median absolute deviation. J Am Stat Assoc 88: 1273–1283
Seki T, Yokoyama S-I (1996) Robust parameter-estimation using the bootstrap method for the 2-parameter Weibull distribution. IEEE Trans Reliab 45: 34–41
Shier D, Lawrence K (1984) A comparison of robust regression techniques for the estimation of Weibull parameters. Commun Stat B Simul Comput 13: 743–750
Shorack GR, Wellner J (1986) Empirical processes with applications to statistics. Wiley, New York
Siegel AF (1982) Robust regression using repeated medians. Biometrika 69: 242–244
Staudte R, Sheather S (1990) Robust estimation and testing. Wiley, New York
Aelst S, Rousseeuw PJ (2000) Robustness of deepest regression. J Multivariate Anal 73: 82–106
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Boudt, K., Caliskan, D. & Croux, C. Robust explicit estimators of Weibull parameters. Metrika 73, 187–209 (2011). https://doi.org/10.1007/s00184-009-0272-1
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00184-009-0272-1