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 |
Files in This Item:
File | Description | Size | Format | |
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DP_0220_SFB823_Klüppelberg_Seifert.pdf | DNB | 400.52 kB | Adobe PDF | View/Open |
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