Exact tests for outliers in Laplace samples

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.

KEYWORDS:

• Critical value
• Discordancy test
• Dixon-type test
• Exponential distribution
• Murphy’s test
• Spacings

Acknowledgments

The authors express their sincere thanks to reviewers for their valuable comments and suggestions on an earlier version of this manuscript which led to this improved version. We also thank Mr. Yen-Chou Chen for the help on numerical checking.

Additional information

Funding

The first author thanks the Ministry of Science and Technology of the Republic of China, Taiwan (Grant No: MOST 108-2118-M-032-002-MY2) for funding this research.