Reconstructing heavy tailed distributions by splicing with maximum entropy in the mean

In this note we propose an application of the method of maximum entropy in the mean to the problem of determining a heavy tailed distribution from its moments. The philosophy consists in proposing a prior distribution, made of two parts that reflect intuitive knowledge about the solution, and then using the method of maximum entropy in the mean to obtain a ``posterior'' (but not in the bayesian sense) distribution, that is absolutely continuous with repct to the prior, that has the same tail behavior as the prior and has two given global moments.