Rescuing MaxEnt

Relevant probability distributions (PDs) in sciences can be obtained by recourse to the constrained maximization of appropriately devised information-entropic functionals. The associated Maximum Entropy formalism (MaxEnt) and its application to the many fields has been the subject of intense activity. However, there lurks the ominous possibility that MaxEnt might be saddled by a basic ambiguity: that any PD might be derivable from the maximization of an arbitrary entropic measure if only an adequate constraint is provided. However, the aforementioned, troublesome ambiguity vanishes from MaxEnt if mono-parametric families of PDs are considered.