Tests for multiple upper or lower outliers in an exponential sample

Abstract

T = \[x + … + x ]/ Sigma x (T*= \[x + … + x ] Sigma x ) is the max k (n- k+ 1 ) (n) i k ( 1 ) (k) i imum likelihood ratio test statistic for k upper ( lower ) outliers in an exponential sample x , …, x . The null distributions of T for k= 1, 2 were given by Fisher and by Kimber 1 n k and Stevens , while those of T*(k= 1, 2) were given by Lewis and Fieller . In this paper , k the simple null distributions of T and T* are found for all possible values of k, and k k percentage points are tabulated for k= 1, 2, …, 8. In addition , we find a way of determining k, which can reduce the masking or ' swamping ' effects .