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 "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".

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 Rothman and Boice (1979) mention that these limits were first proposed by Byar (unpublished).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

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)


[Package DescTools version 0.99.54 Index]