Motivated by and with the aim of generalizing (Bar-Lev and Enis, 1987), we identify various limit laws of certain centralizing transformations of families of random variables by establishing a nontrivial equivalence with limits of their Laplace-Stieltjes transforms evaluated at transformed values.
Bibliographical noteFunding Information:
The second author was supported in part by grant no. 434/09 from the Israel Science Foundation and the Vigevani Chair in Statistics .
- Bernstein functions
- Centralizing transformation
- Infinitely divisible distributions
- Small parameter behavior
- Small time behavior