 On the (Im-)Possibility of Representing Probability Distributions as a Difference of I.I.D. Noise TermsChristian Ewerhart and Marco Serena Working Papers from Max Planck Institute for Tax Law and Public Finance Abstract: A random variable is difference-form decomposable (DFD) if it may be written as the di¤erence of two i.i.d. random terms. We show that densities of such variables exhibit a remarkable degree of structure. Specifically, 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 difference of noise terms rather than on its components. Keywords: Differences of random variables; Density functions; Characteristic function; Uniform distribution (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:mpi:wpaper:tax-mpg-rps-2023-04 Access Statistics for this paper More papers in Working Papers from Max Planck Institute for Tax Law and Public Finance Contact information at EDIRC. |
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