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| Type | Working Paper |
| Scope | Discipline-based scholarship |
| Title | On the (im-)possibility of representing probability distributions as a difference of i.i.d. noise terms |
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| Institution | University of Zurich |
| Series Name | Working paper series / Department of Economics |
| Number | 428 |
| ISSN | 1664-7041 |
| Number of Pages | 29 |
| Date | 2023 |
| Abstract Text | A random variable is difference-form decomposable (DFD) if it may be written as the difference of two i.i.d. random terms. We show that densities of such variables exhibit a remarkable degree of structure. Specifcally, a DFD density can be neither approximately uniform, nor quasiconvex, nor strictly concave. On the other hand, a DFD density need, in general, be neither unimodal nor logconcave. Regarding smoothness, we show that a compactly supported DFD density cannot be analytic and will often exhibit a kink even if its components are smooth. The analysis highlights the risks for model consistency resulting from the strategy widely adopted in the economics literature of imposing assumptions directly on a dfference of noise terms rather than on its components. |
| Free access at | Official URL |
| Other Identification Number | merlin-id:23393 |
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| Keywords | Differences of random variables, density functions, characteristic function, uniform distribution |
| Additional Information | Revised version |