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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.23587 |
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| _version_ | 1866914101521809408 |
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| author | Hansen, Peter Reinhard Tong, Chen |
| author_facet | Hansen, Peter Reinhard Tong, Chen |
| contents | We introduce a novel method for obtaining a wide variety of moments of any random variable with a well-defined moment-generating function (MGF). We derive new expressions for fractional moments and fractional absolute moments, both central and non-central moments. The expressions are relatively simple integrals that involve the MGF, but do not require its derivatives. We label the new method CMGF because it uses a complex extension of the MGF and can be used to obtain complex moments. We illustrate the new method with three applications where the MGF is available in closed-form, while the corresponding densities and the derivatives of the MGF are either unavailable or very difficult to obtain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23587 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Moments by Integrating the Moment-Generating Function Hansen, Peter Reinhard Tong, Chen Econometrics Computational Finance Computation We introduce a novel method for obtaining a wide variety of moments of any random variable with a well-defined moment-generating function (MGF). We derive new expressions for fractional moments and fractional absolute moments, both central and non-central moments. The expressions are relatively simple integrals that involve the MGF, but do not require its derivatives. We label the new method CMGF because it uses a complex extension of the MGF and can be used to obtain complex moments. We illustrate the new method with three applications where the MGF is available in closed-form, while the corresponding densities and the derivatives of the MGF are either unavailable or very difficult to obtain. |
| title | Moments by Integrating the Moment-Generating Function |
| topic | Econometrics Computational Finance Computation |
| url | https://arxiv.org/abs/2410.23587 |