Formulation and Investigation of an Integral Equation for Characteristic Functions of Positive Random Variables

Authors

  • Constantinos T. Artikis Department of Tourism, Faculty of Economic Sciences, Ionian University, 49132 Corfu

DOI:

https://doi.org/10.26713/cma.v12i1.1554

Keywords:

Characteristic function, Random sum, Functional equation

Abstract

Functional equations of characteristic functions constitute power research tools for establishing new results in several significant areas of probability theory. The present paper makes use of the characteristic functions of two Poisson random sums and the concept of equality in distribution for introducing an important selfdecomposable distribution.

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References

M. Alimohammadi and M. H. Alamatsaz, Some new results on unimodality of generalized order statistics and their spacing, Statistics & Probability Letters 81(11) (2011), 1677 – 1682, DOI: 10.1016/j.spl.2011.06.020.

M. Alimohammadi, M. H. Alamatsaz and E. Cramer, Convolutions and generalization of logconcavity: Implications and applications, Naval Research Logistics 63(2) (2016), 109 – 123, DOI: 10.1002/nav.21679.

C. Artikis, Stochastic integrals and power contractions in Bernoulli selections, Journal of Informatics and Mathematical Sciences 10(3) (2018), 411 – 415, DOI: 10.26713/jims.v10i3.909.

C. T. Artikis and P. T. Artikis, Equality in distribution of random sums for introducing selfdecomposabilty, Communications in Mathematics and Applications 11(4) (2020), 559 – 562, DOI: 10.26713/cma.v11i4.1118.

E. Hashorva, A. G. Pakes and Q. Tang, Asymptotics of random contractions, Insurance: Mathematics and Economics 47(3) (2010), 405 – 414, DOI: 10.1016/j.insmatheco.2010.08.006.

V. Korolev and T. Shevtsiva, An improvement of the Berry-Esseen inequality with applications to Poisson and mixed Poisson random sums, Scandinavian Actuarial Journal 2012(2) (2012), 81 – 105, DOI: 10.1080/03461238.2010.485370.

R. Olshen and S. Savage, A generalized unimodality, Journal of Applied Probability 7 (1970), 21 – 34, DOI: 10.2307/3212145.

M. Pinsky and S. Karlin, An Introduction to Stochastic Modeling, 4th edition, Academic Press, Oxford (2011), URL: https://books.google.co.in/books?hl=en&lr=&id=PqUmjp7k1kEC&oi=fnd&pg=PP2&ots=m9jDmsURIa&sig=bOfgh5ITiksXVHaEPbTeUErGxz0#v=onepage&q&f=false.

K.-I. Sato and M. Yamazato, On distribution functions of class L, Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 43 (1978), 273 – 308, DOI: 10.1007/BF00534763.

F. W. Steutel and K. van Harn, Infinite Divisibility of Probability Distributions on the Real Line, Marcel Dekker, Inc., New York (2004), https://books.google.co.in/books?hl=en&lr=&id=5ddskbtvVjMC&oi=fnd&pg=PP1&dq=Infinite+Divisibility+of+Probability+Distributions+on+the+Real+Line&ots=ldczeaetSJ&sig=36Gh7w-9TzohSuHhKYshXe8znuM#v=onepage&q=Infinite%20Divisibility%20of%20Probability%20Distributions%20on%20the%20Real%20Line&f=false.

M. Yamazato, Some results on infinitely divisible distributions of class L with applications to branching process, Science Reports of the Tokyo Kyoiku Daigaku, Section A 13(347/365) (1975), 133 – 139, URL: https://www.jstor.org/stable/43698873.

K. Ziha, Modeling of worsening, Journal of Systemics, Cybernetics and Informatics 10(4) (2012), 11 – 16, URL: http://www.iiisci.org/journal/CV$/sci/pdfs/HNB651OC.pdf.

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Published

31-03-2021
CITATION

How to Cite

Artikis, C. T. (2021). Formulation and Investigation of an Integral Equation for Characteristic Functions of Positive Random Variables. Communications in Mathematics and Applications, 12(1), 199–202. https://doi.org/10.26713/cma.v12i1.1554

Issue

Vol. 12 No. 1 (2021)

Section

Research Article

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