The authors point out that the ''principle of maximum entropy'' can be considered as a variational principle which has applications in statistical mechanics, in decision theory, in pattern-recognition and in time-series analysis. They explain this principle as follows: From the set of all probability distributions (for instance, the possible microscopic states of a system) compatible with one or several mean values of one or several random variables (for instance, the macroscopic energy that is the mean value of the random variable energy which is associated to each microscopic state) choose the one that maximizes the Shannon entropy. Especially, in the case of a discrete random variable whose mean value is given, the authors give the connections of the principle of maximum entropy with Gibbs (canonical) distribution and Laplace's principle of insufficient reason.