distribution - entropy estimation using histogram of normal data vs direct formula (matlab) -


let's assume have drawn n=10000 samples of standard normal distribution.

now want calculate entropy using histograms calculate probabilities.

1) calculate probabilities (for example using matlab)

[p,x] = hist(samples,binnumbers); area = (x(2)-x(1))*sum(p); p = p/area;

(binnumbers determined due rule)

2) estimate entropy

h = -sum(p.*log2(p))

which gives 58.6488

now when use direct formula calculate entropy of normal data

h = 0.5*log2(2*pi*exp(1)) = 2.0471

what do wrong when using histograms + entropy formula? thank help!!

you missing dp term in sum

dp = (x(2)-x(1)); area = sum(p)*dp; h = -sum( (p*dp) * log2(p) );

this should bring close enough...

ps,
careful when take log2(p) might have empty bins. might find nansum useful.


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