Thank you, I really appreciate the response. This was useful.
I do see the reasoning for choosing the normal due to it being the only distribution with finite non-zero moments, and thus, as you nicely pointed out, constraints on a finite number of higher order moments will not give a unique distribution.
But, due to the issues we've now mentioned, I find myself a bit uneasy wrt. maxent as a derivation of and/or as an explanation of the ubiquity of the normal distribution. Thus I find myself more comfortable with some of the other derivations demonstrated by Jaynes.
And thank you for the paper reference; will have a proper look at it sometime. It might be related to
I do see the reasoning for choosing the normal due to it being the only distribution with finite non-zero moments, and thus, as you nicely pointed out, constraints on a finite number of higher order moments will not give a unique distribution.
But, due to the issues we've now mentioned, I find myself a bit uneasy wrt. maxent as a derivation of and/or as an explanation of the ubiquity of the normal distribution. Thus I find myself more comfortable with some of the other derivations demonstrated by Jaynes.
And thank you for the paper reference; will have a proper look at it sometime. It might be related to