Geodesic
On distrubution of Grubbs' statistics in case of normal sample with outlier
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2017), pp. 84-101

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We investigate one-sided Grubbs' statistics for a normal sample. Those statistics are standardized maximum and standardized minimum. i. e. studentized extreme deviation statistics. We consider the case of the sample when there is one abnormal observation (outlier), unknown to what number according. The outlier differs from other observations in values of population mean and dispersion. We obtain recursive relationships for the marginal distribution function of one-sided Grubbs's statistics. We find asymptotic formulas for marginal distribution functions. We obtain recursive relationships for the joint distribution function one-sided Grubbs' statistics. We investigate the properties of the joint distribution function.
Keywords: one-sided Grubbs' statistics, standardized minimum and maximum, outlier, marginal distribution functions, asymptotic approximations, joint distribution function, power functions for Grubbs' criterions.
Mots-clés : normal distribution 
@article{IVM_2017_4_a9,
     author = {L. K. Shiryaeva},
     title = {On distrubution of {Grubbs'} statistics in case of normal sample with outlier},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {84--101},
     publisher = {mathdoc},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_4_a9/}
}
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L. K. Shiryaeva. On distrubution of Grubbs' statistics in case of normal sample with outlier. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2017), pp. 84-101. http://geodesic.mathdoc.fr/item/IVM_2017_4_a9/