R: Poisson Confidence Interval

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 Rothman and Boice (1979) mention that these limits were first proposed by Byar (unpublished).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

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", "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 0.99.25 Index]