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

Department of Statistics

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

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 .

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

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10.1016/j.spl.2012.11.027

Cite this

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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",

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AU - Bar-Lev, Shaul K.

AU - Kella, Offer

AU - Löpker, Andreas

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PY - 2013/3

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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

AN - SCOPUS:84871407930

SN - 0167-7152

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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

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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