Explicit results on conditional distributions of generalized exponential mixtures

Klüppelberg, Claudia; Seifert, Miriam Isabel

Explicit results on conditional distributions of generalized exponential mixtures

dc.contributor.author	Klüppelberg, Claudia
dc.contributor.author	Seifert, Miriam Isabel
dc.date.accessioned	2020-02-14T15:10:11Z
dc.date.available	2020-02-14T15:10:11Z
dc.date.issued	2020
dc.description.abstract	For independent exponentially distributed random variables Xi, i ∈ N with distinct rates λi we consider sums ∑i∈AXi for A⊆N which follow generalized exponential mixture (GEM) distributions. We provide novel explicit results on the conditional distribution of the total sum ∑i∈NXi giventhat a subset sum ∑j∈NXj exceeds a certain threshold value t > 0, and vice versa. Moreover, we investigate the characteristic tail behavior of these conditional distributions for t → ∞,. Finally, we illustrate how our probabilistic results can be applied in practice by providing examples from both reliability theory and risk management.	en
dc.identifier.uri	http://hdl.handle.net/2003/38570
dc.identifier.uri	http://dx.doi.org/10.17877/DE290R-20489
dc.language.iso	en	de
dc.relation.ispartofseries	Discussion Paper / SFB823;2/2020	en
dc.subject	conditional distribution	en
dc.subject	tail behavior	en
dc.subject	risk management	en
dc.subject	reliability theory	en
dc.subject	phase-type distributions	en
dc.subject	generalized exponential mixture distribution	en
dc.subject	exponential distribution	en
dc.subject	convolution	en
dc.subject.ddc	310
dc.subject.ddc	330
dc.subject.ddc	620
dc.subject.rswk	Bedingte Wahrscheinlichkeitsverteilung	de
dc.subject.rswk	Exponentialverteilung	de
dc.subject.rswk	Zusammengesetzte Verteilung	de
dc.title	Explicit results on conditional distributions of generalized exponential mixtures	en
dc.type	Text	de
dc.type.publicationtype	workingPaper	de
dcterms.accessRights	open access
eldorado.secondarypublication	false	de

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