Poisson with unknow parameter and error control
- From: "OT" <montoz@xxxxxx>
- Date: 24 Sep 2006 14:06:19 -0700
Hi all,
I have problems in understanding how to "control" errors done in a
measure process.
Let's say I have a Poisson variable.
If I know the Poisson parameter lambda (i.e. the mean, or the
variance), I can find how many observations I need to be sure that the
arithmetic mean of the observations is close enoght to the expected
value: I can find a number N such that, doing (at least ) N
observations is sufficient to say that
lambda = arithmetic_mean(x_1, x_2, ... , x_N) +- e%
with a given probability.
What I really don't know is how to control error rates when I don't
know the expected value: if I only know that the process is descried by
a Poisson distribution, and if I observe values
x_1, ... x_n , how can I say that the expecte value, lambda, is close
to the arithmetic mean? I.e. how can i find an error e such that
lambda = arithmetic_mean(x_1, x_2, ... , x_N) +- e%
with probability 0,95?
Should I suppose lambda <= Lambda_Max or something similar?
Thanks in advance for every help!
--
andrea
.
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