Author:
Klüppelberg Claudia,Seifert Miriam Isabel
Abstract
AbstractFor independent exponentially distributed random variables
$X_i$
,
$i\in {\mathcal{N}}$
, with distinct rates
${\lambda}_i$
we consider sums
$\sum_{i\in\mathcal{A}} X_i$
for
$\mathcal{A}\subseteq {\mathcal{N}}$
which follow generalized exponential mixture distributions. We provide novel explicit results on the conditional distribution of the total sum
$\sum_{i\in {\mathcal{N}}}X_i$
given that a subset sum
$\sum_{j\in \mathcal{A}}X_j$
exceeds a certain threshold value
$t>0$
, and vice versa. Moreover, we investigate the characteristic tail behavior of these conditional distributions for
$t\to\infty$
. Finally, we illustrate how our probabilistic results can be applied in practice by providing examples from both reliability theory and risk management.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Cited by
6 articles.
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