density estimation: compute sum(value * probability) for given distribution
bogdan romocea wrote:
Dear R users, This is a KDE beginner's question. I have this distribution:
length(cap)
[1] 200
summary(cap)
Min. 1st Qu. Median Mean 3rd Qu. Max.
459.9 802.3 991.6 1066.0 1242.0 2382.0
I need to compute the sum of the values times their probability of
occurence.
The graph is fine,
den <- density(cap, from=min(cap),
to=max(cap), give.Rkern=F)
plot(den)
However, how do I compute sum(values*probabilities)?
I don't get the point. You are estimating using a gaussian kernel. Hint: What's the probability to get x=0 for a N(0,1) distribution? So sum(values*probabilities) is zero! > The
probabilities produced by the density function sum to only 26%:
and could also sum to, e.g., 783453.9, depending on the number of observations and the estimated parameters of the desnity ...
sum(den$y)
[1] 0.2611142 Would it perhaps be ok to simply do
sum(den$x*den$y) * (1/sum(den$y))
[1] 1073.22 ?
No. den$x is a point where the density function is equal to den$y, but den$y is not the probability to get den$x (you know, the stuff with intervals)! I fear you are mixing theory from discrete with continuous distributions. Uwe Ligges
Thank you, b.
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