blyth.still.casella {BlythStillCasellaCI} R Documentation

## Blyth-Still-Casella exact binomial confidence intervals

### Description

computes the Blyth-Still-Casella exact binomial confidence intervals based on a refining procedure proposed by George Casella (1986).

### Usage

```blyth.still.casella(n, X = NULL, alpha = 0.05, digits = 2,
CIs.init = NULL, additional.info = FALSE)
```

### Arguments

 `n` number of trials `X` number of successes (optional) `alpha` confidence level = 1 - alpha `digits` number of significant digits after the decimal point `CIs.init` initial confidence intervals from which the refinement procedure begins (default starts from Clopper-Pearson confidence intervals) `additional.info` additional information about the types of interval endpoints and their possible range is provided if TRUE (default = FALSE)

### Value

If `X` is specified, the corresponding confidence interval will be returned, otherwise a list of n + 1 confidence intervals will be returned.

If `additional.info = FALSE`, only a list of confidence interval(s) will be returned. For any conincidental endpoint, midpoint of its range will be displayed.

If `additional.info = TRUE`, the following lists will be returned:

 `CI` a list of confidence intervals `coinc.index` indices of coincidental lower endpoints (L.Index) and their corresponding upper endpoints (U.index) `endpoint.type` whether the endpoint is coincidental (C) or non-coincidental (NC) `range` range for each endpoint

### Examples

```# to obtain 95% CIs for n = 30 and X = 0 to 30
blyth.still.casella(n = 30, alpha = 0.05, digits = 4)

# to obtain 90% CIs, endpoint types, indices of coincidental enpoints (if any),
# and range of each endpoint for n = 30 and X = 23
blyth.still.casella(n = 30, X = 23, alpha = 0.05, digits = 4, additional.info = TRUE)

# use initial confidence intervals defined by the user instead of Clopper-Pearson CIs
# CIs.input needs to be a (n + 1) x 2 matrix with sufficient coverage
CIs.input <- matrix(c(0,1), nrow = 11, ncol = 2, byrow = TRUE) # start with [0,1] intervals
blyth.still.casella(n = 10, alpha = 0.05, digits = 4, CIs.init = CIs.input, additional.info = TRUE)

# use summary function to see the range for each endpoint
output <- blyth.still.casella(n = 5, alpha = 0.1, digits = 4, additional.info = TRUE)
summary(output)
```

[Package BlythStillCasellaCI version 1.0.0 Index]