Version 1
: Received: 26 April 2024 / Approved: 28 April 2024 / Online: 28 April 2024 (08:28:24 CEST)
How to cite:
Leipus, R.; Šiaulys, J.; Danilenko, S.; Karasevičienė, J. Randomly Stopped Sums, Minima and Maxima for Heavy-tailed and Light-Tailed Distributions. Preprints2024, 2024041843. https://doi.org/10.20944/preprints202404.1843.v1
Leipus, R.; Šiaulys, J.; Danilenko, S.; Karasevičienė, J. Randomly Stopped Sums, Minima and Maxima for Heavy-tailed and Light-Tailed Distributions. Preprints 2024, 2024041843. https://doi.org/10.20944/preprints202404.1843.v1
Leipus, R.; Šiaulys, J.; Danilenko, S.; Karasevičienė, J. Randomly Stopped Sums, Minima and Maxima for Heavy-tailed and Light-Tailed Distributions. Preprints2024, 2024041843. https://doi.org/10.20944/preprints202404.1843.v1
APA Style
Leipus, R., Šiaulys, J., Danilenko, S., & Karasevičienė, J. (2024). Randomly Stopped Sums, Minima and Maxima for Heavy-tailed and Light-Tailed Distributions. Preprints. https://doi.org/10.20944/preprints202404.1843.v1
Chicago/Turabian Style
Leipus, R., Svetlana Danilenko and Jūratė Karasevičienė. 2024 "Randomly Stopped Sums, Minima and Maxima for Heavy-tailed and Light-Tailed Distributions" Preprints. https://doi.org/10.20944/preprints202404.1843.v1
Abstract
This paper investigates the randomly stopped sums, minima and maxima of heavy- and light-tailed random variables. The conditions on the primary random variables, which are independent but generally not identically distributed, and counting random variable are given in order that the randomly stopped sum, random minimum and maximum is heavy/light tailed. The results generalize some existing ones in the literature. The examples illustrating the results are provided.
Keywords
heavy tail; light tail; randomly stopped sums; randomly stopped minima; randomly stopped maxima
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The commenter has declared there is no conflict of interests.
Comment:
Please, cite the following paper related to the topic:
Markovich N.M., Rodionov I.V. Maxima and sums of non-stationary random length sequences. Extremes, 23(3), 451-464 (2020) DOI: 10.1007/s10687-020-00372-5
Commenter:
The commenter has declared there is no conflict of interests.
Markovich N.M., Rodionov I.V. Maxima and sums of non-stationary random length sequences. Extremes, 23(3), 451-464 (2020) DOI: 10.1007/s10687-020-00372-5