Authors: Klüppelberg, Claudia
Seifert, Miriam Isabel
Title: Explicit results on conditional distributions of generalized exponential mixtures
Language (ISO): en
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.
Subject Headings: conditional distribution
tail behavior
risk management
reliability theory
phase-type distributions
generalized exponential mixture distribution
exponential distribution
convolution
Subject Headings (RSWK): Bedingte Wahrscheinlichkeitsverteilung
Exponentialverteilung
Zusammengesetzte Verteilung
URI: http://hdl.handle.net/2003/38570
http://dx.doi.org/10.17877/DE290R-20489
Issue Date: 2020
Appears in Collections:Sonderforschungsbereich (SFB) 823

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