On the stability of characterizations by an identical distribution property |
| |
| Authors: | R. Yanushkevichius O. Yanushkevichiene |
| |
| Affiliation: | (1) Institute of Mathematics of Ukrainian National Academy of Sciences, 01601 Kyiv, Ukraine;(2) Department of Mathematical Analysis Faculty of Mechanics and Mathematics, National Taras Shevchenko University of Kyiv, 01033 Kyiv, Ukraine;(3) Department of Probability Theory and Mathematical Statistics Faculty of Mechanics and Mathematics, National Taras Shevchencko University of Kyiv, 01033 Kyiv, Ukraine |
| |
| Abstract: | Let X 1, X 2, … , X n be i.i.d. random variables with common distribution F, and let b 1, b 2, … , b n be real coefficients such that ∑ b j 2 = 1. We prove that F is close to the normal distribution in the Lévy metric whenever the distribution of the linear statistic ∑ b j X j is close to F. |
| |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ |
|
