Small parameter behavior of families of distributions

Shaul K. Bar-Lev; Offer Kella; Andreas Löpker

doi:10.1016/j.spl.2012.11.027

Small parameter behavior of families of distributions

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

University of Haifa, The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	783-789
Number of pages	7
Journal	Statistics and Probability Letters
Volume	83
Issue number	3
DOIs	https://doi.org/10.1016/j.spl.2012.11.027
State	Published - Mar 2013

Keywords

Bernstein functions
Centralizing transformation
Infinitely divisible distributions
Small parameter behavior
Small time behavior

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

Access to Document

10.1016/j.spl.2012.11.027

Cite this

@article{b17289ed1f174184a6555199b2a80e06,

title = "Small parameter behavior of families of distributions",

abstract = "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.",

keywords = "Bernstein functions, Centralizing transformation, Infinitely divisible distributions, Small parameter behavior, Small time behavior",

author = "Bar-Lev, \{Shaul K.\} and Offer Kella and Andreas L{\"o}pker",

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 .",

year = "2013",

month = mar,

doi = "10.1016/j.spl.2012.11.027",

language = "English",

volume = "83",

pages = "783--789",

journal = "Statistics and Probability Letters",

issn = "0167-7152",

publisher = "Elsevier B.V.",

number = "3",

}

TY - JOUR

T1 - Small parameter behavior of families of distributions

AU - Bar-Lev, Shaul K.

AU - Kella, Offer

AU - Löpker, Andreas

N1 - 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 .

PY - 2013/3

Y1 - 2013/3

N2 - 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.

AB - 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.

KW - Bernstein functions

KW - Centralizing transformation

KW - Infinitely divisible distributions

KW - Small parameter behavior

KW - Small time behavior

UR - https://www.scopus.com/pages/publications/84871407930

U2 - 10.1016/j.spl.2012.11.027

DO - 10.1016/j.spl.2012.11.027

M3 - Article

SN - 0167-7152

VL - 83

SP - 783

EP - 789

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 3

ER -

Small parameter behavior of families of distributions

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this