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On distribution of Grubbs’ statistics in case of normal sample with outlier. (English. Russian original) Zbl 1458.62042

Russ. Math. 61, No. 4, 72-88 (2017); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2017, No. 4, 84-101 (2017).
Summary: We investigate one-sided F. E. Grubbs’ statistics for a normal sample [Ann. Math. Stat. 21, 27–58 (1950; Zbl 0036.21003)]. 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’ statistics. We find asymptotic formulas for marginal distribution functions. We obtain recursive relationships for the joint distribution function of one-sided Grubbs’ statistics and investigate its properties.

MSC:

62D05 Sampling theory, sample surveys
60E10 Characteristic functions; other transforms

Citations:

Zbl 0036.21003
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Full Text: DOI

References:

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