The Use in Probabilistic Design of Probability Curves Generated by Maximizing the Shannon Entropy Function Constrained by Moments

Abstract

A general algorithm is described for obtaining the maximum entropy distribution constrained by moments in functional form. It is based on Jaynes’ principle. The distribution is proposed as a useful tool in probabilistic design. The maximum entropy distribution is generated for a large number of analytical distributions, and compared with the original. The results appear to confirm that it can represent well most populations when four or five moments are used. The maximum entropy distribution is also compared with the Johnson and Pearson empirical distributions. The results are favorable in the two examples given. The practical convenience of the method in probabilistic design is illustrated by an example in structures.