PoissonCI: Poisson Confidence Interval
In DescTools: Tools for Descriptive Statistics

PoissonCI

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 Rothman and Boice (1979) mention that these limits were first proposed by Byar (unpublished).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

https://www.ine.pt/revstat/pdf/rs120203.pdf

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)

DescTools documentation built on Sept. 26, 2024, 1:07 a.m.