On Detecting Multiple Outliers in Gamma Samples

In this paper, we suggest the test statistic for detecting multiple outliers in gamma distribution and derive its probability density function using characteristic function. Since the probability density function of the proposed function is very complicative, from simulation study, we present the critical values of the proposed test statistics to detect outliers easily. We also compare the powers of the proposed test statistic with other comparative statistics, Dixon (1950)’s statistic, Nooghabi et al. (2010)‘s statistic, Kumar, Lalitha (2012)’s statistic, Kim, Kim (2015)’s statistic. Throughout the simulation studies, we show that our proposed test statistic has good powers among other statistics. In particular we can inspect that the powers of our proposed test statistics are relatively good when the number of outliers, k, is greater than or equal to 2. As we know, an exponential distribution is a special case of a gamma distribution, therefore the results in this paper are applicable to an exponential distribution.