density estimate

Mon, Sep 29, 2008 8:10 AM

The calculation of the Kullback Leibler measure depends on the scale of 
your probability function. If it is discrete, the formula with "sum" 
term applies. In the continuous case "sum" is replaced by "intgrate".
you may have a look at 
http://finzi.psych.upenn.edu/R/library/flexmix/html/KLdiv.html which 
covers both cases.
For continuous random variables you can typically get only probability 
statements for intervals - by integrating the density function over the 
range of the given interval. If your sample space is uncountable (say 
for instance the set of all real numbers), then it can be shown that 
every elementary event has to have a probability of zero.

hth.

Sumithran schrieb:

Thank you. 

I need the probability, because I'm trying to get the Kullback Leibler measure between two densities. Is there any package which gives the probability function for continuous distributions?


Thaks,

Lavan

--- On Mon, 9/29/08, Eik Vettorazzi <E.Vettorazzi at uke.uni-hamburg.de> wrote:

From: Eik Vettorazzi <E.Vettorazzi at uke.uni-hamburg.de>
Subject: Re: [R]  density estimate
To: "Lavan" <rsumithran at yahoo.com>
Cc: r-help at r-project.org
Date: Monday, September 29, 2008, 7:39 AM
Hi Lavan,
a continuous density is not restricted to be within [0, 1].
Its only 
bound to have an integral of 1.
For example
dnorm(0,sd=.1)
is a very common density and gives 3.989423. A density
function is not a 
probability function!
If you think your data x is discrete than you can assign
the correct 
probability mass for each data point by
 prop.table(table(x))

hth.

Lavan schrieb:

Hi,

I have a vector or random variables and I'm

estimating the density using

"bkde" function in the KernSmooth package.

The out put contains two vectors

(x and y), and the R documentation calls y as the

density estimates, but my

y-values are not exact density etstimates (since these

are numbers larger

than 1)! what is y here? Is it possible to get the

true estimated density at

each value of x?

Thanks

-- 
Eik Vettorazzi
Institut f?r Medizinische Biometrie und Epidemiologie
Universit?tsklinikum Hamburg-Eppendorf

Martinistr. 52
20246 Hamburg

T ++49/40/42803-8243
F ++49/40/42803-7790

Eik Vettorazzi
Institut f?r Medizinische Biometrie und Epidemiologie
Universit?tsklinikum Hamburg-Eppendorf

Martinistr. 52
20246 Hamburg

T ++49/40/42803-8243
F ++49/40/42803-7790