Copyright © 2009 Henryk Gzyl and Enrique Ter Horst. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present a new method, based on the method of maximum entropy in the mean, which builds upon the standard method of maximum entropy, to improve the parametric estimation of a decay rate when the measurements are corrupted by large level of noise and, more importantly, when the number of measurements is small. The method is developed in the context on a concrete example: that of estimation of the parameter in an exponential distribution. We show how to obtain an estimator with the noise filtered out, and using simulated data, we compare the performance of our method with the Bayesian and maximum likelihood approaches.