Abstract
Let Φ(X) be a measurable complex function on R;X, Y, Z be i.i.d. random variables; and φ{symbol}(t, u, v)=EΦ(tX+uY+nZ), where t, u, v∈R. In this paper we describe a class of function Φ(x) such that the distribution of X, Y, Z is determined by the funetion φ{symbol}(t, u, v). The main result is a generalization of the author's characterization of normal and stable distributions.
| Original language | English |
|---|---|
| Pages (from-to) | 691-700 |
| Number of pages | 10 |
| Journal | Journal of Theoretical Probability |
| Volume | 4 |
| Issue number | 4 |
| DOIs | |
| State | Published - 1 Oct 1991 |
| Externally published | Yes |
Keywords
- Distribution
- characterization
- function
- random variables
ASJC Scopus subject areas
- Statistics and Probability
- Mathematics (all)
- Statistics, Probability and Uncertainty