1. Gnedenko, B.V. 1989. Ob otsenke neizvestnykh parametrov raspredeleniya pri sluchaynom chisle nezavisimykh nablyudeniy [On estimate of unknown distribution parameters in case of random number of independent values]. Tbilisi Mathematical Institute 92:146-150.
2. Korolev, V.Yu. 2013. Obobshchennye giperbolicheskie raspredeleniya kak predel'nye dlya sluchaynykh summ [Generalized hyperbolic distributions as limiting for random sums] Theory Probab. Appl. 58(1):117-132.
3. Zaks, L.M., and V.Yu. Korolev. 2013. Obobshchennye dispersionnye gamma- raspredeleniya kak predel'nye dlya sluchaynykh summ [Generalized variance gamma distributions as limiting for random sums]. Informatika i ee Primeneniya - Inform. Appl. 7(1):105-115.
4. Korolev, V.Yu., and A. I. Zeifman. 2015 (in press). On convergence of the distributions of statistics constructed from samples with random sizes to normal variance-mean mixtures. J. Stat. Planning Inference. Available at: arXiv:1410.1518v1 [math.PR].
5. Antonov, S.N., and S.N. Koksharov. 2006. Ob asimptoticheskom povedenii khvostov masshtabnykh smesey normalnykh raspredeleniy [On asimptotic behavior of tails of normal variance mixtures]. Statisticheskiye metody otsenivaniya i proverki gipotez [Statistical methods for estimation and hypothesis validation]. Perm: Perm University Press. 90-105.
6. Loeve, M. 1955. Probability theory. Princeton, NJ: D Van Nostrand. 702 p.
7. Barndorff-Nielsen, O. E. 1977. Exponentially decreasing distributions for the logarithm of particle size. Proc. Roy. Soc. Lond. A 353:401-419.
8. Barndorff-Nielsen, O. E. 1978. Hyperbolic distributions and distributions of hyperbolae. Scand. J. Stat. 5:151-157.
9. Barndorff-Nielsen, O. E., J. Kent, and M. S rensen. 1982. Normal variance-mean mixtures and z-distributions. Int. Stat. Rev. 50(2):145-159.
10. Jorgensen, B. 1982. Statistical properties of the generalized inverse Gaussian distribution. Lecture notes in statistics ser. Berlin: Springer. Vol. 9. 188 p.
11. Stacy, E.W. 1962. A generalization of the gamma distribution. Ann. Math. Stat. (33):1187-1192.
12. Korolev, V.Yu., A.Yu. Korchagin, and A. I. Zeifman. 2015 (in press). O skhodimosti raspredeleniy statistik, postroennykh po vyborkam sluchaynogo ob'yema, k mnogomernym obobshchennym dispersionnym gamma-raspredeleniyam [On convergence of the distributions of statistics constructed fromsamples with random sizes tomultivariate generalized variance-gamma distributions].Dokl. Akad. nauk [Acad. Sci. Rep.] 462(4).
13. Billingsley, P. 1968. Convergence of probability measures. New York, NY: Wiley. 353 p.
14. Zolotarev, V.M. 1997. Modern theory of summation of random variables. Utrecht: VSP. 412 p.
15. Kruglov, V.M. 1973. Skhodimost' chislovykh kharakteristik summ nezavisimykh sluchaynykh velichin so znacheniyami v gil'bertovom prostranstve [Convergence of numerical characteristics of sums of independent random variables with values in Hilbert space]. Theory Probab. Appl. 18(3):734-752.
16. Gikhman, I. I., and A.V. Skorokhod. 1971. Teoriya sluchaynykh protsessov [Theory of random processes]. Moscow: Nauka. 665 p.

Title

ON CONVERGENCE OF RANDOM SUMS OF INDEPENDENT RANDOM VECTORS TO MULTIVARIATE GENERALIZED VARIANCE-GAMMA DISTRIBUTIONS

Journal

Systems and Means of Informatics
Volume 25, Issue 1, pp 127-141

Cover Date

2013-11-30

DOI

10.14357/08696527150108

Print ISSN

0869-6527

Publisher

Institute of Informatics Problems, Russian Academy of Sciences

Additional Links

• Editorial Board
• About This Journal
• Manuscript Submission

Key words

random sum; multivariate normal variance-mean mixture; multivari- ate generalized hyperbolic distribution; multivariate generalized variance-gamma distribution; generalized inverse Gaussian distribution; generalized gamma dis- tribution

Authors

A. Yu. Korchagin

Author Affiliations

   Faculty of Computational Mathematics and Cybernetics, M.V. Lomonosov Moscow State University, 1-52 Leninskiye Gory, GSP-1, Moscow 119991, Russian Federation