Small parameter behavior of families of distributions

Shaul K. Bar-Lev, Offer Kella, Andreas Löpker*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageAmerican English
Pages (from-to)783-789
Number of pages7
JournalStatistics and Probability Letters
Issue number3
StatePublished - Mar 2013

Bibliographical note

Funding 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


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