We focus on the whole range of data, whose upper tail follows a power-law behavior.
We modeled the exponent of the Power Law distribution using a non-linear function.
We found a new family of Generalized Power Law (GPL) distributions.
We studied a relevant model of that family, the <em>GPLem>(<em>α, β, σem>) distribution.
<em>GPLem>(<em>α, β, σem>) dist. can be useful for modeling municipal debt data in the whole range.