Publication Date



Technical Report: UTEP-CS-24-02


In many practical situations, we only have partial information about the probability distribution -- e.g., all we know is its few moments. In such situations, it is desirable to select one of the possible probability distributions. A natural way to select a distribution from a given class of distributions is the maximum entropy approach. For the case when we know the first two moments, this approach selects the normal distribution. However, when we also know the third central moment -- corresponding to skewness -- a direct application of this approach does not work. Instead, practitioners use several heuristic techniques, techniques for which there is no convincing justification. In this paper, we show that while we cannot directly apply the maximum entropy approach to the skewness situation, we can apply it approximately -- with any approximation accuracy we want -- and get a meaningful answer to the above selection problem.