Abstract
A general discussion and survey is provided of the characterization of the normal distribution by the identical distribution of linear forms. The first result dates to 1923 when Pólya showed that if X and Y are i.i.d. random variables satisfying certain conditions, and if aX + bY is distributed as (a2 + b2)1/2X, then X has a normal distribution. This result has been generalized in several directions. In addition to a recasting of some of the results, an extension in the multivariate case is provided.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Reference10 articles.
1. Bemerkung zur charackterisierung des Gauszschen Fehlergesetzes;Vincze;Magyar Tud. Akad. Mat. Kutató Int. Közl.,1962
2. Herleitung des Gau�schen Fehlergesetzes aus einer Funktionalgleichung
3. Linear forms and statistical criteria;Linnik;Ukrain. Mat. Zurnal,1953
4. A generalization of a theorem of E. Vincze;Laha;Magyar Tud. Akad. Mat. Kutató, Int. Közl.,1964
5. On a linear form whose distribution is identical with that of a monomial
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献