The aim of this note is to characterize a class of distributions whose characteristic functions ?(t) for all ? > 0 satisfy the relation
?t?R
where H and H? are positive real constants. First, it is observed that these distributions turn out to belong to the well-known class of infinitely divisible distributions. More specifically, they are strictly stable and thus absolutely continuous, self-decomposable and unimodal. But they are not strongly unimodal except for the case of H=2H. Then some representations are obtained for ?(t). Finally, some characterizations are arrived at for the Cauchy and N (0, ?¬2); 0< ?¬2 < ?; distributions.
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