Normality via conditional normality of linear forms

Abram Kagan and Jacek Wesolowski

Statistics & Probability Letters, 1996, vol. 29, issue 3, 229-232

Abstract: It is proved that if the conditional distribution of one linear form in two independent (not necessarily identically distributed) random variables given another is normal, then the variables are normal. The result complements a series of characterizations of normal distribution via different properties of linear forms: independence, linearity of regression plus homoscedasticity, equidistribution, conditional symmetry and normality. The method is different from previous ones and is based on properties of densities, not characteristic functions.

Keywords: Normal; distribution; Normal; conditional; distribution; Linear; forms; Conditional; specifications; of; probability; distributions (search for similar items in EconPapers)
Date: 1996
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