DescTools (version 0.99.19)

PoissonCI: 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, method = c("exact", "score", "wald"))

Arguments

x

number of events.

n

time base for event count.

conf.level

confidence level, defaults to 0.95.

method

character string specifing which method to use; can be one out of "wald", "score". Method can be abbreviated. See details. Defaults to "score".

Value

A vector with 3 elements for estimate, lower confidence intervall and upper for the upper one.

Details

The Wald interval uses the asymptotic normality of the test statistic.

References

Agresti, A. and Coull, B.A. (1998) Approximate is better than "exact" for interval estimation of binomial proportions. American Statistician, 52, pp. 119-126.

Garwood, F. (1936) Fiducial Limits for the Poisson distribution. Biometrika 28:437-442.

http://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"))

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)