Exact computation of the null distribution of a test for multiple outliers in an exponential sample

Through a systematic application of the recursion of Huffer [Huffer, F., 1988. Divided differences and the joint distribution of linear combinations of spacings. Journal of Applied Probability 25, 346-354], we present an algorithm for evaluating the exact null distribution of the test statistic proposed by Kimber [Kimber, A.C., 1982. Tests for many outliers in an exponential sample. Applied Statistics 31, 263-271] for the testing of up to k upper outliers for discordancy in exponential samples. This method presents another way of obtaining the exact null distribution of the test statistic without first obtaining their joint density. The advantage of this approach is in its generality and also in its ease of use. In addition, it can provide critical values for the test statistic that are accurate to any required degree of precision. Similar results for the sequential testing of up to k lower outliers for discordancy are also presented.