defined can be combined. The convolution is a bilinear operation (Schwartz, 1966, p.157); convolution of a tensor product of generalized functions on two vector spaces, R $^{d$_{1}$}$,Rd$_{2}$ is the tensor product of the convolutions of functions in each space (Schwartz, 1966, p.158). Moreover convolution of any number of generalized functions can be defined in D ∗ as long as all except possibly one have compact supports and this operation is associative and commutative (Schwartz, 1966, p.158); a variable shift or derivative of a convolution exists and is obtained by a shift or differentiation of any of the generalized functions entering the convolution (Schwartz, 1966, p.160). Note that if ( A,B ) is a convolution pair then ( A ∪ G,B ∪ G ) is also a convolution pair. All the pairs of spaces in the Table satisfy this definition. This assumption implies that (2) holds; it is often satisfied in statistical problems. Convolution of generalized density functions exists, thus (1) leads to (2) for all distributions even when the density functions do not exist in the ordinary sense. The finite sum of δ − functions considered by Klann et al (2007) is in E $^{∗}$, thus convolution with any element of D ∗ (or S $^{∗}$) exists 20 Definition Call a pair of subspaces of generalized functions, A ⊂ G ∗ and B ⊂ G ∗ a convolution pair ( A,B ) if for any a ∈ A,b ∈ B convolution a ∗ b is defined in G $^{∗}$; it is a hypocontinuous operation in the topology of G $^{∗}$. Assumption 2. The statistical model defines functions, g and f in G ∗ such that g ∈ A ⊂ G ∗ and f ∈ B ⊂ G $^{∗}$; the subspaces ( A,B ) form a convolution pair.