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Characterization of normal distribution related to two samples based on regression. (English) Zbl 1105.62015
Summary: Characterization of normal distributions related to two samples based on second conditional moments has been obtained. This characterization has been transformed to a characterization based on the UMVU estimators of the density function. These results are generalized to $$k$$ samples from normal distributions. Finally, applications of these characterization results to goodness-of-fit test are discussed.
MSC:
 62E10 Characterization and structure theory of statistical distributions 62F03 Parametric hypothesis testing 62G10 Nonparametric hypothesis testing
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References:
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