Detection of outliers in poisson samples

Abstract

This paper is concerned with the detection of a single (upper or lower) outlier in a Poisson sample. A conditional test due to Doornbos (1966) is discussed and some unconditionaltests based on the original and transformed data are developed. Of the unconditional tests the critical values of the likelihood ratio statistic LRT and the statistic M based on adjusted standardized residuals show dependence on the Poisson Parameter. The Dixon-type statistics based on transformed sample produce critical values which are nearly parameter-independent and in reasonably close agreement with those from the normal distribution. For reasons of simplicity and power we recommend using the statistic T(T^∗) for detecting an upper (lower) outlier, where and x-_i ∼ Poisson (λ). This recommendation falls in line with Barnett and Lewis (1978).

Keywords:

• conditional test
• unconditional test
• transformation to normality
• dixon-type statistics