  Estimating entropies from limited data series is known to be a non-trivial
task. Naive estimations are plagued with both systematic (bias) and statistical
errors. Here, we present a new 'balanced estimator' for entropy functionals
Shannon, R\'enyi and Tsallis) specially devised to provide a compromise between
low bias and small statistical errors, for short data series. This new
estimator out-performs other currently available ones when the data sets are
small and the probabilities of the possible outputs of the random variable are
not close to zero. Otherwise, other well-known estimators remain a better
choice. The potential range of applicability of this estimator is quite broad
specially for biological and digital data series.
