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Download a pdf copy of this help file here |
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Download a pdf copy of this help file here |
We have already given classical statistics techniques for determining confidence
distributions for l
and for b
from a Poisson
process. However, l and b are just the reciprocal
of each other:
b = 1/l
Thus, an interesting question is: Does our estimate vary depending on the method used?
Let's assume that the Poisson process is about events occurring over a period of time t. The estimate for b considers the time between consecutive events ({ti}, so built into that analysis is the assumption that the last of the a events was observed at a moment equal to the sum of all the individual times (t = SUM({ti}).
The estimate for l however considers a total amount of time t and the number of events within that time a. There is no assumption that the last event occurred at time t, so t in this analysis in all probability included some amount of time, from the last event to the finish, when nothing happened.
Thus a/t, the observed rate will be higher in the b estimating scenario than in the l estimating scenario. That means that the b method will systematically estimate a lower value for l (=1/b) than the l estimating method. Of course, the difference becomes progressively smaller the larger the number of events a.