Chia C Chong <[EMAIL PROTECTED]> wrote in message
a1bpk5$62b$[EMAIL PROTECTED]">news:a1bpk5$62b$[EMAIL PROTECTED]...
>
> "Glen" <[EMAIL PROTECTED]> wrote in message
> [EMAIL PROTECTED]">news:[EMAIL PROTECTED]...
> > "Chia C Chong" <[EMAIL PROTECTED]> wrote in message
> news:<a0n001$b7v$[EMAIL PROTECTED]>...
> > > I plotted a histogram density of my data and its smooth version using
> the
> > > normal kernel function. I tried to plot the estimated PDF (Laplacian &
> > > Generalised Gaussian) estimated using maximum likelihood method on top
> as
> > > well. Graphically, its seems that Laplacian wil fit thr histogram
> density
> > > graph better while the Generalised Gaussian will fit the smooth version
> > > (i.e. the kernel densoty version).
> > >
> >
> > Imagine that you began with a sample from a Laplacian (double
> > exponential) distribution. What will happen to the central peak after
> > you smooth it with a KDE?
>
> The peak does not changed significantly...Maybe shifted to the left a
> bit...not too much!!
No, I was not talking about your data, since you don't necessarily have
Laplacian - that's what you're trying to decide!
Imagine you have data actually from a Laplacian distribution.
(It has a sharp peak in the middle, and exponential tails.)
Now you smooth it (KDE via gaussian kernel).
What happens to the peak? (assume a typical window width)
[Answer? It gets smoothed, so it no longer looks like a sharp peak.]
That's where your impression of a gaussian-looking KDE is probably coming from.
Note that the tails of a normal and a laplace are different, so if those are
the two choices, that may help.
Glen
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