On the characteristic function of the joint limit distribution of the first- and second-order power sums

Gy Michaletzky, L. Szeidl, P. Várlaki

Research output: Contribution to journalArticle

Abstract

In this paper we investigate the joint limit characteristic function of normalized first and second-order power sums for a sequence of i.i.d. random variables with distributions belonging to the domain of attraction of an α-stable law for α <2. An explicit form is presented in terms of generalized hypergeometric functions when 0 <α <2, α ≠ 1, and that of Fresnel functions S and C for α = 1.

Original languageEnglish
Pages (from-to)126-135
Number of pages10
JournalTheory of Probability and its Applications
Volume43
Issue number1
Publication statusPublished - Mar 1998

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Power Sum
Generalized Hypergeometric Function
Stable Laws
I.i.d. Random Variables
Domain of Attraction
Limit Distribution
Characteristic Function
Joint Distribution
First-order
Form
Hypergeometric functions
Characteristic function
Random variables
Attraction
Limit distribution

Keywords

  • Domain of attraction of α-stable law
  • Fresnel S and C functions
  • Generalized hypergeometric functions
  • Limit characteristic function
  • Normalized power sums
  • Schrödinger equation

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

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