Convolution and convolution-root properties of long-tailed distributions
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| 008 | 210128e20151201xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s10687-015-0224-2 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10687-015-0224-2 | ||
| 245 | 0 | 0 | |a Convolution and convolution-root properties of long-tailed distributions |h [Elektronische Daten] |c [Hui Xu, Sergey Foss, Yuebao Wang] |
| 520 | 3 | |a We obtain a number of new general properties, related to the closedness of the class of long-tailed distributions under convolutions, that are of interest themselves and may be applied in many models that deal with "plus” and/or "max” operations on heavy-tailed random variables. We analyse the closedness property under convolution roots for these distributions. Namely, we introduce two classes of heavy-tailed distributions that are not long-tailed and study their properties. These examples help to provide further insights and, in particular, to show that the properties to be both long-tailed and so-called "generalised subexponential” are not preserved under the convolution roots. This leads to a negative answer to a conjecture of Embrechts and Goldie (J. Austral. Math. Soc. (Ser. A) 29, 243-256 1980, Stoch. Process. Appl. 13, 263-278 1982) for the class of long-tailed and generalised subexponential distributions. In particular, our examples show that the following is possible: an infinitely divisible distribution belongs to both classes, while its Lévy measure is neither long-tailed nor generalised subexponential. | |
| 540 | |a Springer Science+Business Media New York, 2015 | ||
| 690 | 7 | |a Long-Tailed distribution |2 nationallicence | |
| 690 | 7 | |a Generalised subexponential distribution |2 nationallicence | |
| 690 | 7 | |a Closedness |2 nationallicence | |
| 690 | 7 | |a Convolution |2 nationallicence | |
| 690 | 7 | |a Convolution root |2 nationallicence | |
| 690 | 7 | |a Random sum |2 nationallicence | |
| 690 | 7 | |a Infinitely divisible distribution |2 nationallicence | |
| 690 | 7 | |a Lévy measure |2 nationallicence | |
| 700 | 1 | |a Xu |D Hui |u School of Mathematical Sciences, Soochow University, 215006, Suzhou, China |4 aut | |
| 700 | 1 | |a Foss |D Sergey |u School of MACS and Maxwell Institute, Heriot-Watt University, EH14 4AS, Edinburgh, UK |4 aut | |
| 700 | 1 | |a Wang |D Yuebao |u School of Mathematical Sciences, Soochow University, 215006, Suzhou, China |4 aut | |
| 773 | 0 | |t Extremes |d Springer US; http://www.springer-ny.com |g 18/4(2015-12-01), 605-628 |x 1386-1999 |q 18:4<605 |1 2015 |2 18 |o 10687 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10687-015-0224-2 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10687-015-0224-2 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Xu |D Hui |u School of Mathematical Sciences, Soochow University, 215006, Suzhou, China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Foss |D Sergey |u School of MACS and Maxwell Institute, Heriot-Watt University, EH14 4AS, Edinburgh, UK |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Wang |D Yuebao |u School of Mathematical Sciences, Soochow University, 215006, Suzhou, China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Extremes |d Springer US; http://www.springer-ny.com |g 18/4(2015-12-01), 605-628 |x 1386-1999 |q 18:4<605 |1 2015 |2 18 |o 10687 | ||