Slash distributions, generalized convolutions, and extremes

M. Arendarczyk (), T. J. Kozubowski () and A. K. Panorska ()
Additional contact information
M. Arendarczyk: University of Wrocław
T. J. Kozubowski: University of Nevada
A. K. Panorska: University of Nevada

Annals of the Institute of Statistical Mathematics, 2023, vol. 75, issue 4, No 3, 593-617

Abstract: Abstract An $$\alpha$$ α -slash distribution built upon a random variable X is a heavy tailed distribution corresponding to $$Y=X/U^{1/\alpha }$$ Y = X / U 1 / α , where U is standard uniform random variable, independent of X. We point out and explore a connection between $$\alpha$$ α -slash distributions, which are gaining popularity in statistical practice, and generalized convolutions, which come up in the probability theory as generalizations of the standard concept of the convolution of probability measures and allow for the operation between the measures to be random itself. The stochastic interpretation of Kendall convolution discussed in this work brings this theoretical concept closer to statistical practice, and leads to new results for $$\alpha$$ α -slash distributions connected with extremes. In particular, we show that the maximum of independent random variables with $$\alpha$$ α -slash distributions is also a random variable with an $$\alpha$$ α -slash distribution. Our theoretical results are illustrated by several examples involving standard and novel probability distributions and extremes.

Keywords: Extreme value theory; Generalized convolution; Heavy tails; Kendall convolution; Pareto distribution; Slash distribution (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10463-022-00858-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:aistmt:v:75:y:2023:i:4:d:10.1007_s10463-022-00858-y

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10463/PS2

DOI: 10.1007/s10463-022-00858-y

Access Statistics for this article

Annals of the Institute of Statistical Mathematics is currently edited by Tomoyuki Higuchi

More articles in Annals of the Institute of Statistical Mathematics from Springer, The Institute of Statistical Mathematics
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().