I have a histogram based off of collected data. I can fit the data using a series of Poisson distributions where the fitted values are amplitude (A) and the average (µ). If I do a least-squares fit of the data using one Poisson I get Χ²= 2.05, if I use 2 Poisson's I get Χ²= 0.29, and if I use 3 or more Poisson's I get a Χ²~0.13.
How does one go about estimating the Shannon entropy for the collected data? I can look at the Χ² and I think I can say that using one Poisson is two points of information (A, and µ). Adding a second Poisson helps but is there really two more pieces of information? And adding a third reduces the Χ² but more than three doesn't help at all.How to determine the Shannon Entropy using chi-squared
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