# PoissonCI: Poisson Confidence Interval

### Description

Computes the confidence intervals of a poisson distributed variable's lambda. Several methods are implemented, see details.

### Usage

 `1` ```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"`.

### Details

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

### 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.

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

`poisson.test`, `BinomCI`, `MultinomCI`

### Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```# 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) ```

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