Abstract
There are many random phenomena such that their probability distributions
are not Gaussian but other particular distributions with fat tail. They are the
so-called fractional power distributions. We can see that their mathematical models
can, in some favorable cases, be embedded in stable stochastic processes, which are expressed
as superpositions of Poisson processes with various magnitudes of jump. Thus,
our mathematical theory, which characterizes latent traits of Poisson noise, would effectively
be applied to the random phenomena in question, in order to describe their
biological characteristics.
