Explicit results on conditional distributions of generalized exponential mixtures
| Autor: | Claudia Klüppelberg, Miriam Isabel Seifert |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Reliability theory 021103 operations research Exponential distribution General Mathematics 0211 other engineering and technologies Probabilistic logic 02 engineering and technology Conditional probability distribution 01 natural sciences Exponential function Convolution 010104 statistics & probability Applied mathematics Subset sum problem 0101 mathematics Statistics Probability and Uncertainty Random variable Mathematics |
| Zdroj: | Journal of Applied Probability. 57:760-774 |
| ISSN: | 1475-6072 0021-9002 |
| DOI: | 10.1017/jpr.2020.26 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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