On the distribution of a test statistic for outlier identication in exponential samples

In this paper we discuss the distribution of the ratio of the maximum and the appropriately standardized median of a (sub-) sample consisting of the m smallest observations in a sample of size N coming from a one-parameter exponential distribution. A statistics of this kind is useful when testing for the presence of outliers, especially when implemented within an inward or outward testing procedure. Besides giving a tractable expression for the survival function of this statistic we tabulate the critical values needed for corresponding outlier identification rules for samples of size up to N = 50