Abstract
AbstractZerbet and Nikulin (Commun Statist Theor Meth 32(3): 573–583, 2003) presented the new statistic $${Z}_{k}$$
Z
k
for detecting outliers in exponential distribution. They also compared this statistic with Dixon's statistic $${D}_{k}$$
D
k
. Jabbari et al. (Commun Statist Theor Meth 39(4): 698–706, 2010) expend this statistic ($${Z}_{k}$$
Z
k
) for Gamma distribution. In this paper, we generalize statistics $${Z}_{k}$$
Z
k
–$${Z}_{k}^{*}$$
Z
k
∗
, for detecting outliers in Rayligh distribution and compare the results with the generalized Dixon's statistic. Distribution of the test based on the statistic $${Z}_{k}^{*}$$
Z
k
∗
under slippage alternatives is obtained. The criterion value and power of the new test are also calculated and compared with the criterion value of the Dixon's statistic. The results show that the test based on statistic $${Z}_{k}^{*}$$
Z
k
∗
is more powerful than the test based on the statistic $${D}_{k}$$
D
k
.
Publisher
Springer Science and Business Media LLC
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