In:
Journal of Applied Probability, Cambridge University Press (CUP), Vol. 57, No. 3 ( 2020-09), p. 760-774
Abstract:
For 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.
Type of Medium:
Online Resource
ISSN:
0021-9002
,
1475-6072
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
2020
detail.hit.zdb_id:
1474599-9
detail.hit.zdb_id:
219147-7
SSG:
3,2
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