  It is well known that to estimate the Shannon entropy for symbolic sequences
accurately requires a large number of samples. When some aspects of the data
are known it is plausible to attempt to use this to more efficiently compute
entropy. A number of methods having various assumptions have been proposed
which can be used to calculate entropy for small sample sizes. In this paper,
we examine this problem and propose a method for estimating the Shannon entropy
for a set of ranked symbolic natural events. Using a modified
Zipf-Mandelbrot-Li law and a new rank-based coincidence counting method, we
propose an efficient algorithm which enables the entropy to be estimated with
surprising accuracy using only a small number of samples. The algorithm is
tested on some natural sequences and shown to yield accurate results with very
small amounts of data.
