Abstract

The exact null distributions of test statistics used for testing up to $k(\ge 1)$ upper outliers in a two-parameter Laplace sample are investigated. Two types of test statistics, namely, the modified Murphy’s test for k upper normal outliers and the general Dixon-type test statistic discussed by Childs, are considered. Utilizing the result of conditional independence of blocked ordered data established by Iliopoulos and Balakrishnan, together with the computational algorithm of Huffer and Lin for distributions of linear combinations of exponential variables, exact critical values of test statistics for testing discordancy of k upper outliers in two-parameter Laplace samples are obtained. For illustration, some examples with pertinent computational details are finally presented.

摘要

用于测试的测试统计量的精确零分布$ķ(\ge 1)$研究了两参数拉普拉斯样本中的上异常值。考虑了两种类型的检验统计量，即针对k上正态异常值的修正墨菲检验和 Childs 讨论的一般 Dixon 型检验统计量。利用 Iliopoulos 和 Balakrishnan 建立的阻塞有序数据的条件独立性结果，以及 Huffer 和 Lin 的计算算法，用于指数变量的线性组合分布，测试统计量的精确临界值用于测试k上异常值在两个-获得参数拉普拉斯样本。为了说明，最后给出了一些具有相关计算细节的例子。