`fcci`

is an R package providing support for building Feldman-Cousins
confidence intervals.

The Feldman-Cousins construction was originally developed in the context of High-Energy Physics, as a consistent method for building classical (frequentist) confidence intervals for Poisson rates of rare events. In experiments which expect only few events, it is often the case that the number of observed events is actually zero or, more generally, lower than the expected number of spurious background events (if the latter is significantly larger than zero).

In these situations, classical central intervals (such as those
produced by `stats::poisson.test()`

) are not satisfying, as
they can lead both to significant overcoverage and to non-physical
negative rates in the presence of a non-negligible background. Moreover,
a naive special treatment of boundary values, which chooses to report an
upper limit or a confidence interval depending on the data (the
so-called “flip-flopping”
policy), can lead to undercoverage.

Feldman and Cousins provide a unified treatment of boundary and regular values, by explicitly constructing the Neyman confidence belt for physical rates, using an ordering for count values based on a likelihood ratio.

You can install the latest release of `fcci`

from CRAN using:

`install.packages("fcci")`

and the development version from my R-universe with:

`install.packages("fcci", repos = "https://vgherard.r-universe.dev/")`

`library(fcci)`

To compute a confidence interval for, e.g., a Poisson rate, use:

```
# 95% C.L. interval for n = 10 events and b = 2 expected background events
confint_pois(n = 10, b = 2, cl = 0.95)
#> [1] 2.9205 15.8130
#> attr(,"cl")
#> [1] 0.95
```

Let us compare the 68% C.L. intervals for *n* = 0 events and
no background obtained from `fcci`

and from
`stats::poisson.test()`

```
confint_pois(n = 0, cl = 0.68)
#> [1] 0.000 1.275
#> attr(,"cl")
#> [1] 0.68
::poisson.test(0, conf.level = 0.68, alternative = "two.sided")$conf.int
stats#> [1] 0.000000 1.832581
#> attr(,"conf.level")
#> [1] 0.68
```

Notice that the latter is significantly larger, and it corresponds in
fact to an 84% C.L. *upper limit* on the rate:

```
::poisson.test(0, conf.level = 0.84, alternative = "less")$conf.int
stats#> [1] 0.000000 1.832581
#> attr(,"conf.level")
#> [1] 0.84
```

For further help, you can consult the reference page of the
`fcci`

website
or open an issue
on the GitHub repository of `fcci`

.