DescTools (version 0.99.57)

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, sides = c("two.sided","left","right"),
          method = c("exact", "score", "wald", "byar"))

Value

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

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 "two.sided" (default), "left" or "right". You can specify just the initial letter. "left" would be analogue to a hypothesis of "greater" in a t.test.

method

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

Author

Andri Signorell <[e-mail]>

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 Rothman and Boice (1979) mention that these limits were first proposed by Byar (unpublished).

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.

Rothman KJ, Boice JD, Jr. (1979) Epidemiologic Analysis with a Programmable Calculator (NIH Publication 79-1649). Washington DC: US Government Printing Office.

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

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(DescTools::hred, DescTools::hblue), main = "Deaths from Horse Kicks", 
  xlab = "count")
legend("topright", legend=c("observed","expected"), 
  fill=c(DescTools::hred, DescTools::hblue), bg="white")


## SMR, Welsh Nickel workers
PoissonCI(x=137, n=24.19893)