Abstract
We discuss some simple statistical models leading to some families of probability distributions. These models are of specific interest because the desirable statistical property leads to functional equations having a large set of solutions. It appears that a small subset only of the set of all the solutions has probabilistic sense.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bradley, B.O., Taqqu, M.S.: Financial risk and heavy tails. In: Handbook of Heavy Tailed Distributions in Finance, pp. 35–103 (2003). doi:10.1016/B978-044450896-6.50004-2
Gnedenko, B.V.: On some stability theorems. Lecture Notes Math. 982, 24–31 (1983)
Gnegenko, B.V., Yu Korolev, V.: Random Summation. Limit Theorems and Applications. CRC Press, Boca Raton (1996)
Karlin, S., Studden, W.J.: Tchebycheff Systems: with Applications in Analysis and Statistics. Interscience Publishers, New York (1966)
Klebanov, L.B., Manija, G.M., Melamed, J.A.: A problem by V.M. Zolotarev and analogous of infinitely divisible and stable distributions in the scheme of summation of a random number of random variables. Teor. Verojatnst. i Primenen. 29(4), 757–759 (1984)
Klebanov, L.B., Manija, G.M., Melamed, J.A.: \(\nu _p\)-strictly stable laws and estimation of their parameters. Lecture Notes in Mathematics, vol. 1233, pp. 23–31. Springer, Berlin (1987)
Klebanov, L.B., Rachev, S.T.: Sums of a random number of random variables an their approximations with \(\nu \)- accompanying infinitely divisible laws. Serdica Math. J. 22(4), 471–496 (1996)
Klebanov, L.B., Kakosyan, A.V., Rachev, S.T., Temnov, G.: On a class of distributions stable under random summation. J. Appl. Probab. 49, 303–318 (2012)
Klebanov, L.B., Volchenkova, I. Heavy Tailed Distributions in Finance: Reality or Myth? Amateurs Viewpoint, pp. 1–17 (2015). arXiv: 1507.07735v1
Acknowledgements
Bloomberg dataset and Forbes dataset are data sets containing capitals of top 201 and 100 billionaires, respectively, and were extracted from the official web sites of Bloomberg (www.bloomberg.com) and Forbes (www.forbes.com) in year 2015. The work was partially supported by Grant GACR 16-03708S.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Klebanov, L.B. (2017). Stability and Heavy-Tailness. In: Antoch, J., Jurečková, J., Maciak, M., Pešta, M. (eds) Analytical Methods in Statistics. AMISTAT 2015. Springer Proceedings in Mathematics & Statistics, vol 193. Springer, Cham. https://doi.org/10.1007/978-3-319-51313-3_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-51313-3_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-51312-6
Online ISBN: 978-3-319-51313-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)