Do you desperately need to estimate the entropy of a discrete distribution from data? You’re in luck.
PYMentropy is a MATLAB package providing routines to compute the Bayes’ least squares estimate (i.e., posterior mean) of the entropy of a discrete distribution from samples under a Pitman-Yor Mixture (PYM) prior. The PYM prior is a mixture of Pitman-Yor (or 2-parameter Poisson-Dirichlet) distributions over countably infinite discrete distributions, with mixing weights set to produce an approximately flat prior over entropy. Also computes the posterior variance for quantifying uncertainty.
Archer E, Park IM, Pillow JW (2014). Bayesian entropy estimation for countable discrete distributions. Journal of Machine Learning Research (JMLR), 15 (Oct): 2833-2868.
Archer E, Park I, Pillow JW (2012). Bayesian estimation of discrete entropy with mixtures of stick-breaking priors. Advances in Neural Information Processing Systems (NIPS) 25.