Order Statistics from a Sample Containing a Single Outlier

Abstract

Density functions and joint density functions of order statistics arising from a sample containing a single outlier have been given by Shu (1978) and David and Shu (1978), and have been made use of by David et al. (1977) in tabulating means, variances and covariances of order statistics from a normal sample comprising one outlier. One may also refer to Vaughan and Venables (1972) for more general expressions of distributions of order statistics when the sample, in fact, includes k outliers. The importance of a systematic study of the order statistics from an outlier model and the usefulness of the tables of means, variances and covariances of these order statistics in the context of robustness has been well demonstrated by several authors including Andrews et al. (1972), David and Shu (1978), David (1981), and Tiku et al. (1986).