R help - Nov 2008 - Confidence limits for the parameter of the Poisson distribution

Hi all,
  So far I only know one way to get the confidence limit for the Poisson
distribution is to use the look-up table given by the 2 parameter (the
number of observation x and the confidence level, e.g. 95%) and the table is
limit by the maximum number of observations (x <= 50).
  I know the formula to compute the CI, however, mathematically it is not
easy to do it. So, anyone know an R function to do this. Thanks

Tuan.

	[[alternative HTML version deleted]]

On Thu, 6 Nov 2008, Hoang Trong Minh Tuan wrote:
> Hi all,
>  So far I only know one way to get the confidence limit for the Poisson
> distribution is to use the look-up table given by the 2 parameter (the
> number of observation x and the confidence level, e.g. 95%) and the table
is
> limit by the maximum number of observations (x <= 50).
>  I know the formula to compute the CI, however, mathematically it is not
> easy to do it. So, anyone know an R function to do this. Thanks

A 'marriage-of-convenience' between uniroot() and ppois() should do it.

HTH,

Chuck

>
> Tuan.
>
> 	[[alternative HTML version deleted]]
>
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Charles C. Berry                            (858) 534-2098
                                             Dept of Family/Preventive Medicine
E mailto:cberry at tajo.ucsd.edu	            UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/  La Jolla, San Diego 92093-0901

On 7/11/2008, at 9:26 AM, Hoang Trong Minh Tuan wrote:
> Hi all,
>   So far I only know one way to get the confidence limit for the  
> Poisson
> distribution is to use the look-up table given by the 2 parameter (the
> number of observation x and the confidence level, e.g. 95%) and the  
> table is
> limit by the maximum number of observations (x <= 50).
>   I know the formula to compute the CI, however, mathematically it  
> is not
> easy to do it. So, anyone know an R function to do this. Thanks
>
> Tuan.
You may find the URL

	http://www.math.mcmaster.ca/peter/s743/poissonalpha.html

useful.

	cheers,

		Rolf Turner

P.S.  The foregoing URL discusses the issues in terms of a *single*
observation.  Note that if X_1, ..., X_n are i.i.d. Poisson(lambda)
then Y = X_1 + ... + X_n is Poisson(n*lambda).

Note that the ``exact'' confidence limits are very conservative.

		R. T.

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