PoissonCI {DescTools}  R Documentation 
Computes the confidence intervals of a poisson distributed variable's lambda. Several methods are implemented, see details.
PoissonCI(x, n = 1, conf.level = 0.95, sides = c("two.sided","left","right"),
method = c("exact", "score", "wald", "byar"))
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

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 Rothman and Boice (1979) mention that these limits were first proposed by Byar (unpublished).
A vector with 3 elements for estimate, lower confidence intervall and upper for the upper one.
Andri Signorell <andri@signorell.net>
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
poisson.test
, BinomCI
, MultinomCI
# 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)