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.