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STABLE PARETIAN DISTRIBUTIONS
Because it is a special case, to distinguish between normal and nonnormal stable distributions, the latter are often referred to as stable Paretian distributions.
One attack on the stable Paretian distribution was that there is no closed-form solution to obtain the necessary information about the distribution-probability density and distribution functions.
The major attack in the 1970s and 1980s centered around the claim that while the empirical evidence does not support the normal distribution, it is also not consistent with the stable Paretian distribution.
For example, it was observed that asset return distributions are not as heavy-tailed as the stable Paretian distribution would predict.
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