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Normality via conditional normality of linear forms


  • Kagan, Abram
  • Wesolowski, Jacek


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.

Suggested Citation

  • Kagan, Abram & Wesolowski, Jacek, 1996. "Normality via conditional normality of linear forms," Statistics & Probability Letters, Elsevier, vol. 29(3), pages 229-232, September.
  • Handle: RePEc:eee:stapro:v:29:y:1996:i:3:p:229-232

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    References listed on IDEAS

    1. E. Castillo & J. Galambos, 1989. "Conditional distributions and the bivariate normal distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 36(1), pages 209-214, December.
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