Poisson with unknow parameter and error control

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?

Thanks in advance for every help!

--
andrea

.

Relevant Pages

  • Re: Poisson with unknow parameter and error control
    ... If I know the Poisson parameter lambda (i.e. the mean, ... x_n, how can I say that the expecte value, lambda, is close ... appropriate control is to stop when the total ...
    (sci.stat.math)
  • Re: Poisson with unknow parameter and error control
    ... If I know the Poisson parameter lambda (i.e. the mean, ... x_n, how can I say that the expecte value, lambda, is close ... appropriate control is to stop when the total ...
    (sci.stat.math)
  • Poisson with unknow parameter and error control
    ... Let's say I have a Poisson variable. ... If I know the Poisson parameter lambda (i.e. the mean, ... What I really don't know is how to control error rates when I don't ... x_n, how can I say that the expecte value, lambda, is close ...
    (sci.stat.edu)
  • Re: Question about use of Poisson probabilities
    ... Probability theory was never my forte. ... I'm glad you're not going to call your boss an idiot. ... are a Poisson process, then 700,000 shows much, much, much too ... assumptions about your distribution that you need in order ...
    (sci.math)
  • Re: Question about use of Poisson probabilities
    ... James, my knowledge of probability theory is weak, and I'm no mathematical ... What do you mean by poisson and normal statistics? ...
    (microsoft.public.excel.misc)