Re: Some Paradox on Confidence Interval of Population Parameter!
- From: undiscern <undiscern@xxxxxxxxx>
- Date: 21 May 2007 18:36:44 -0700
These are some more example info:
Lets say I have failure data for everyday and Im tracking the Rate of
change in Sum Yi. Yi = Xi/N
GRAPH 1
-------
SUM *
Yi | * *
| * *
| *
| *
|
| *
|*
|______________________________
1 2 3 4 5 6 7 8 9 10 11 12 ... (Calendar Day 2005)
GRAPH 2
-------
Ri,
Rate of Change of Sum Yi
|
|
|
|
|
|
| * * *
|* * **
| ***
|______________________________
1 2 3 4 5 6 7 8 9 10 11 12 ... (Calendar Day 2005)
Frequentist
------------
Since Yi is the population parameter for day i, it is a constant
according to frequentist. Hence there should not be any confidence
interval on CI.
Since Yi has no interval, Ri has no interval too?
If Ri has no interval, how do we know that there is indeed a shift in
Ri?
Bayesian
---------
Yi though is a population parameter, it is not a constant and has a
distribution. For example if Y1 ~ N (2,1) Y2 ~ N(3, 1.2) ...
Implying Graph 1 plot of Yi is the mean of its distribution.
Therefore
the 95% confidence interval for Y1 is 2 +- 1.96 Sqrt(1/M).
Is M = N???
.
- References:
- Some Paradox on Confidence Interval of Population Parameter!
- From: undiscern
- Some Paradox on Confidence Interval of Population Parameter!
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