A characterization of the normal law

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1969 English Publisher:Springer Science and Business Media LLCJournal:Annals of the Institute of Statistical Mathematics, volume 21, pages 529-532 (issn: 0020-3157, eissn: 1572-9052,

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Authors: Pakshirajan, R. P.; Mohan, N. R.;

doi: 10.1007/bf02532276

A characterization of the normal law

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Abstract

IfX, Y, Z are three random observations from a normal population with mean zero then the characteristic function of (X/Z, Y/Z) is exp\(( - \sqrt {t^2 + u^2 } )\). It is shown in this paper that this property characterizes the normal law.

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University of Mysore
India

Keywords

Characterization and structure theory of statistical distributions

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