Publication: On the (im-)possibility of representing probability distributions as a difference of i.i.d. noise terms
On the (im-)possibility of representing probability distributions as a difference of i.i.d. noise terms
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Ewerhart, C., & Serena, M. (2023). On the (im-)possibility of representing probability distributions as a difference of i.i.d. noise terms (No. 428; Working Paper Series / Department of Economics).
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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 ar
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Ewerhart, C., & Serena, M. (2023). On the (im-)possibility of representing probability distributions as a difference of i.i.d. noise terms (No. 428; Working Paper Series / Department of Economics).
