Tests for a Single Upper Outlier in a Johnson SB Sample with Unknown Parameters

Abstract

Outliers are unexpected observations, which deviate from the majority of observations. Outlier detection and prediction are challenging tasks, because outliers are rare by definition. A test statistic for single upper outlier is proposed and applied to Johnson SB sample with unknown parameters. The Johnson SB distribution have four parameters and is extremely flexible, which means that it can fit a wide range of distribution shapes. Because of its distributional shapes it has a variety of applications in many fields. The test statistic proposed for the case when parameters are known (Sriwastava, T., 2018) used here for developing the test statistic when parameters are unknown. Critical points were calculated for different sample sizes and for different level of significance. The performance of the test in the presence of a single upper outlier is investigated. One numerical example was given for highlighting the result.