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Continuity Properties of Distributions with Some Decomposability

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Abstract

Absolute continuity and smoothness of distributions in the nested subclasses ~L m(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 ~L m(B) are absolutely continuous and the minimum integer m for which all absolutely continuous distributions in ~L m(B) have the densities of class C r for 0 ≤ r ≤ ∞ are discussed according to the type of the matrix B related to P.V. numbers.

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Authors
  1. Toshiro Watanabe
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Watanabe, T. Continuity Properties of Distributions with Some Decomposability. Journal of Theoretical Probability 13, 169–191 (2000). https://doi.org/10.1023/A:1007739010953

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