First thing you probably should realize is that density is _not_
probability. A probability density function _integrates_ to one,
not _sum_
to one. If X is an absolutely continuous RV with density f, then
Pr(X=x)=0
for all x, and Pr(a < X < b) = \int_a^b f(x) dx.
sum x*Pr(X=x) (over all possible values of x) for a discrete
distribution is
just the expectation, or mean, of the distribution. The
expectation for a
continuous distribution is \int x f(x) dx, where the integral is
over the
support of f. This is all elementary math stat that you can find
in any
textbook.
Could you tell us exactly what you are trying to compute, or why
you're
computing it?
HTH,
Andy
From: bogdan romocea
Dear R users,
This is a KDE beginner's question.
I have this distribution:
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
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)? The
probabilities produced by the density function sum to only 26%:
[1] 0.2611142
Would it perhaps be ok to simply do
sum(den$x*den$y) * (1/sum(den$y))
[1] 1073.22
?
Thank you,
b.