Re: First order variation in PDF
- From: illywhacker <illywacker@xxxxxxxxx>
- Date: Fri, 7 Nov 2008 01:46:53 -0800 (PST)
On Oct 13, 6:24 am, JunoExpress <MTBrenne...@xxxxxxxxx> wrote:
Hi,
Consider a pdf having compact support on [-X,+X] for some given
positive real X, that is a function of a real parameter c.
When c=0, the pdf is symmetric about x=0 and the pdf takes a very
simple form.
When c is non-zero, the form of the pdf is non-zymmetric about x=0
becomes quite complicated.
I want to understand the effect c has when it is small but non-zero,
on the bias of x.
One way I considered was to construct an approximation to the pdf:
(1) f(x,c) \approx f(x,o) + c (df/dc)at c=0
Now the RHS of (1) integrates to 1, but it is probably not a pdf
(since it is not obvious the first order approx is non-negative). This
bothers me somewhat, and has me wondering if this is the correct way
to approach this problem. Any suggestions?
TIA,
Matt
Is positivity really that important if the approximation is good?
Alternatively, positivity is a condition on c that should be satisfied
at least for c small enough.
illywhacker;
.
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