Linear combination of bilateral gamma random variables: distributional theory and approximations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917358165032960 |
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| author | Barman, Kalyan Vellaisamy, Palaniappan |
| author_facet | Barman, Kalyan Vellaisamy, Palaniappan |
| contents | In this article, we obtain the exact distribution of a linear combination of bilateral gamma (BG) random variables (r.v.s). Next, we discuss the distributional properties of the linear combination of BG r.v.s, including probability density function, cumulant generating function and characteristic function. A Stein characterization is developed, which leads us to several distributional approximation results with explicit error bounds in both Kolmogorov and Wasserstein distances. Related limit theorems are also discussed. Furthermore, we show that the associated Lévy processes are finite-variation processes with BG distributed increments having random parameters. Finally, we apply our results in exponential stock models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_22112 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Linear combination of bilateral gamma random variables: distributional theory and approximations Barman, Kalyan Vellaisamy, Palaniappan Probability 62E15, 62E17, 62P05, 60E05, 60E07 In this article, we obtain the exact distribution of a linear combination of bilateral gamma (BG) random variables (r.v.s). Next, we discuss the distributional properties of the linear combination of BG r.v.s, including probability density function, cumulant generating function and characteristic function. A Stein characterization is developed, which leads us to several distributional approximation results with explicit error bounds in both Kolmogorov and Wasserstein distances. Related limit theorems are also discussed. Furthermore, we show that the associated Lévy processes are finite-variation processes with BG distributed increments having random parameters. Finally, we apply our results in exponential stock models. |
| title | Linear combination of bilateral gamma random variables: distributional theory and approximations |
| topic | Probability 62E15, 62E17, 62P05, 60E05, 60E07 |
| url | https://arxiv.org/abs/2603.22112 |