ISC2007 , 2007-05-31

#### Title : ( A New Statistic for Detecting Outliers in Gamma Distribution )

Authors: Hadi Jabbari Nooghabi , Mehdi Jabbari Nooghabi ,

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~~~~Bol\'shev \\cite{Bol\'shev} generalized the Chauvenet\'s test for rejecting outlier observations (see Bol\'shev \\cite{Bol\'shev} and Voinov and Nikulin \\cite{Voinov and Nikulin 1996})\\textbf{.} This method is suitable for detecting $k$ outliers in an univariate data set. The Chauvenet\'s test can be used for exponential case. Also, Ibragimov and Khalfina \\cite{Ibragimov and Khalfina} considered various modification of this test. Several authors considered the problem for testing one outlier in exponential distribution Chikkagoudar and Kunchur \\cite{Chikkagoudar and Kunchur}, Lewis and Fiellerm \\cite{Lewis and Fiellerm}, Likes \\cite{Likes} and Kabe \\cite{Kabe}. Only two types of statistics for testing multiple outliers exist. First is Dixon\'s while the second is based on the ratio of the some 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 \\textbf{as} a special case. This approach is focused on alternative models, namely slippage alternatives in exponential samples (see Barnett and Toby Lewis \\cite{Barnett and Toby Lewis}). Zerbet and Nikulin \\cite{Zerbet and Nikulin} proposed a statistic different from the well known \\textit{Dixon\'s statistic} $D_k$ to test for multiple outliers. ~~~~In this paper, we extend the statistic $Z_k$ proposed by Zerbet and Nikulin \\cite{Zerbet and Nikulin} for Gamma distribution. Distribution of the test based on this statistic under slippage alternatives is obtained and the tables of critical values are given for various $n$ (size of the sample) and $k$ (the number of outliers). The power of this test is also calculated, it is compared to the power of the Dixon\'s statistic (Chikkagoudar and Kunchur \\cite{Chikkagoudar and Kunchur}). The test based on statistic $Z_k$ is more powerful than the test based on the Dixon\'s statistic.

#### Keywords

, outliers, Gamma
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@inproceedings{paperid:1008593,
author = {Jabbari Nooghabi, Hadi and Mehdi Jabbari Nooghabi},
title = {A New Statistic for Detecting Outliers in Gamma Distribution},
booktitle = {ISC2007},
year = {2007},
location = {بمبئی, INDIA},
keywords = {outliers; Gamma distribution},
}

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%0 Conference Proceedings
%T A New Statistic for Detecting Outliers in Gamma Distribution
%A Jabbari Nooghabi, Hadi
%A Mehdi Jabbari Nooghabi
%J ISC2007
%D 2007

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