Continuity Properties of Distributions with Some Decomposability
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Absolute continuity and smoothness of distributions in the nested subclasses ~Lm(B), m = 0, 1, 2,..., of the class of all B-decomposable distributions are studied. All invertible matrices are classified into two types in terms of P.V. numbers. The minimum integer m for which all full distributions in ~Lm(B) are absolutely continuous and the minimum integer m for which all absolutely continuous distributions in ~Lm(B) have the densities of class Cr for 0 ≤ r ≤ ∞ are discussed according to the type of the matrix B related to P.V. numbers.
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