A new statistic for detecting outliers in exponential case

A generalization of Chauvenet's test (see Bol'shev, L. N. (1969). On tests for rejecting outlying observations. Trudy In-ta prikladnoi Mat. Tblissi Gosudart. univ. 2:159-177. (In Russian); Voinov, V. G., Nikulin, M. N. (1996). Unhaised Estimators and Their Applications. Vol. 2. Kluwer Academic Publishers.) suitable to applied the problem of detecting r outliers in an univariate data set is proposed. In the exponential case, the Chauvenet's test can be used. Various modifications of this test were considered by Bol'shev, Ibrakimov and Khalfina (Ibrakimov, I. A., Khalfina (1978). Some asymptotic results concerning the Chauvenet test. Ter. Veroyatnost. i Primenen. 23(3):593-597.), Greenwood and Nikulin (Greenwood, Nikulin, P. E. (1996). A Guide to Chi-Squared Testing New York: John Wiley and Sons, Inc.) depending on the choice of the estimation method used: MLE or MVUE. As procedures for testing one outlier in exponential model have been investigated by a number of authors including Chikkagoudar and Kunchur (Chikkagoudar, M. S., Kunchur, S. H. (1983). Distribution of test statistics for multiple outliers in exponential samples. Comm. Stat. Theory. and Meth. 12:2127-2142.), Lewis and Fieller (Lewis, T., Fiellerm N. R. J. (1979). A recursive algorithm for null distribution for outliers : I. Gamma samples. Technometrics 21:371-376.), Likes (Likes, J. (1966). Distribution of Dixon's statistics in the case of an exponential population. Metrika 11:46-54. (91, 96, 136, 198-200, 204, 209, 2 10).) and Kabe (Kabe, D. G. (1970). Testing outliers from an exponential population. Metrika 15:15-18.); only two types of statistics for testing multiple outliers exist. First is Dixon's while the second is based on the ratio of the sum of the observations suspected to be outliers to the sum of all observations of the sample. In fact, most of these authors have considered a general case of gamma model and the results for exponential model are given a special case. The object of the present communication is to focus on alternative models, namely slippage alternatives (see Barnett, Vic., Toby Lewis (1978). Outlier in Statistical Data. New York: John Wiley and Sons, Inc.) in exponential samples. We propose a statistic different from the well known Dixon's statistic D, to test for multiple outliers. Distribution of the test based on this new statistic under slippage alternatives is obtained and hence the tables of critical values are given, for various n (size of the sample) and r (the number of outliers). The power of the new test is also calculated, it is compared to the power of the Dixon's statistic (Chikkagoudar, M. S., Kunchur, S. H. (1983). Distribution of test statistics for multiple outliers in exponential samples. Comm. Stat. Theory. and Meth. 12:2127-2142.). Notice that the new statistic based test power is greater the Dixon's statistic based test one.