Three estimators for the entropy of continuous random variables (one dimension)
entropy_bin()uses the common histogram approach. In addition to the data, it requires specifying a bin width.entropy_ci()uses the first order correlation integral, which is like a niave kernel density estimator. In addition to the data, it required specifying a neighborhood radius (kernel bandwidth), which analogous to a (half) bin width for the histogram estimator.entropy_nn()uses the distribution of nearest neighbor distances. It requires no adjustable parameters.
Using some simulations with various bandwidths, my experience is that the nearest neighbor estimator has the lowest bias, but the highest variance. The correlation integral estimator is probably the best, especially with a well chosen neighbor radius. The histogram methods tends to underestimate the entropy. I suspect a kernel density estimator using a gaussian kernel would be even better, but that is not implemented.