A broad set of sufficient conditions that guarantees the existence of themaximum entropy (maxent) distribution consistent with specified bounds oncertain generalized moments is derived. Most results in the literature areeither focused on the minimum cross-entropy distribution or apply only todistributions with a bounded-volume support or address only equalityconstraints. The results of this work hold for general moment inequalityconstraints for probability distributions with possibly unbounded support, andthe technical conditions are explicitly on the underlying generalized momentfunctions. An analytical characterization of the maxent distribution is alsoderived using results from the theory of constrained optimization ininfinite-dimensional normed linear spaces. Several auxiliary results ofindependent interest pertaining to certain properties of convex coercivefunctions are also presented.
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