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
=
Instructions for joining and leaving this list, remarks about the
problem of INAPPROPRIATE MESSAGES, and archives are available at
http://jse.stat.ncsu.edu/
=
