electron energy distributions

[LL-RL]

Dear zbla,
By studying your open source SED fitting tool, I have some questions to ask you.
(1) For what kind of physical cases are the different electron energy spectrum distributions in the tool, i.e. PowerLaw, ExponentialCutoffPowerLaw, BrokenPowerLaw, ExponentialCutoffBroken、PowerLaw and LogParabola given?
I am interested to know how these above forms of electron energy spectrum are derived physically and mathematically?
Best.
Lu Lin