SupplementalMaterial

In (28), the normalizing termAα(θ) is inside the (2 α)-exponential. In (30), there is an normalizingfactorBα(θ)outsidetheα-exponential. Naturally, whenα = 1, these two problems become equivalent, since an additive term inside the exponential is equivalent to a multiplicative term outside. QuotingNaudts[10, 1]: "An important question is then whether in the modification the normalization should stand infront ofthe deformed exponential function, or whether itshould be included aslnZ(β) inside. Since each slice of aparaboloid is an ellipsoid, we can apply Cavalieri's principle to obtain the volume of a paraboloidy = 12x>Σ 1x of height h = λ as follows: Vpar(h) = Z h Now we show that a solution always exists ifg is strongly convex,i.e., if there is someγ > 0 such that g(0) g(s) sg0(s)+ γ2s2 foranys 0. LetF(s):= sg0(s) g(s)+g(0).