[R] density estimation: compute sum(value * probability) for given distribution

[Uwe Ligges]

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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