Joint confidence region estimation of L-moment ratios with an extension to right censored data

Abstract

L-moments, defined as specific linear combinations of expectations of order statistics, have been advocated by Hosking 7 and others in the literature as meaningful replacements to that of classic moments in a wide variety of applications. One particular use of L-moments is to classify distributions based on the so-called L-skewness and L-kurtosis measures and given by an L-moment ratio diagram. This method parallels the classic moment-based plot of skewness and kurtosis corresponding to the Pearson system of distributions. In general, these methods have been more descriptive in nature and failed to consider the corresponding variation and covariance of the point estimators. In this note, we propose two procedures to estimate the 100(1−α)% joint confidence region of L-skewness and L-kurtosis, given both complete and censored data. The procedures are derived based on asymptotic normality of L-moment estimators or through a novel empirical characteristic function (c.f.) approach. Simulation results are provided for comparing the performance of these procedures in terms of their respective coverage probabilities. The new and novel c.f.-based confidence region provided superior coverage probability as compared to the standard bootstrap procedure across all parameter settings. The proposed methods are illustrated via an application to a complete Buffalo snow fall data set and to a censored breast cancer data set, respectively.

Keywords:

• L-moment
• inversion theorem
• characteristic function
• bootstrap
• asymptotic normality

Acknowledgements

The authors are grateful to the editor and three anonymous referees for their critical and constructive comments.