PoissonCI {DescTools}  R Documentation 
Poisson Confidence Interval
Description
Computes the confidence intervals of a poisson distributed variable's lambda. Several methods are implemented, see details.
Usage
PoissonCI(x, n = 1, conf.level = 0.95, sides = c("two.sided","left","right"),
method = c("exact", "score", "wald", "byar"))
Arguments
x 
number of events. 
n 
time base for event count. 
conf.level 
confidence level, defaults to 0.95. 
sides 
a character string specifying the side of the confidence interval, must be one of 
method 
character string specifing which method to use; can be one out of

Details
The Wald interval uses the asymptotic normality of the test statistic.
Byar's method is quite a good approximation. Rothman and Boice (1979) mention that these limits were first proposed by Byar (unpublished).
Value
A vector with 3 elements for estimate, lower confidence intervall and upper for the upper one.
Author(s)
Andri Signorell <andri@signorell.net>
References
Agresti, A. and Coull, B.A. (1998) Approximate is better than "exact" for interval estimation of binomial proportions. American Statistician, 52, pp. 119126.
Rothman KJ, Boice JD, Jr. (1979) Epidemiologic Analysis with a Programmable Calculator (NIH Publication 791649). Washington DC: US Government Printing Office.
Garwood, F. (1936) Fiducial Limits for the Poisson distribution. Biometrika 28:437442.
https://www.ine.pt/revstat/pdf/rs120203.pdf
See Also
poisson.test
, BinomCI
, MultinomCI
Examples
# the horse kick example
count < 0:4
deaths < c(144, 91, 32, 11, 2)
n < sum(deaths)
x < sum(count * deaths)
lambda < x/n
PoissonCI(x=x, n=n, method = c("exact","score", "wald", "byar"))
exp < dpois(0:4, lambda) * n
barplot(rbind(deaths, exp * n/sum(exp)), names=0:4, beside=TRUE,
col=c(hred, hblue), main = "Deaths from Horse Kicks", xlab = "count")
legend("topright", legend=c("observed","expected"), fill=c(hred, hblue),
bg="white")
## SMR, Welsh Nickel workers
PoissonCI(x=137, n=24.19893)