  We introduce a class of probability measures whose densities near infinity
are mixtures of Pareto distributions. This class can be characterized by the
Fourier transform which has a power series expansion including real powers, not
only integer powers. This class includes stable distributions in probability
and also non-commutative probability theories. We also characterize the class
in terms of the Cauchy-Stieltjes transform and the Voiculescu transform. If the
stability index is greater than one, stable distributions in probability theory
do not belong to that class, while they do in non-commutative probability.
