WbinoCI {ExactCIone}

An Admissible Exact Confidence Interval for the Bnomial Proportion

Description

An admissible exact confidence interval of level 1-alpha is constructed for the binomial proportion p. This function can be used to calculate the interval constructed method proposed by Wang (2014).

Usage

WbinoCI(x, n, conf.level = 0.95, details = FALSE)

Arguments

x

the number of success or the observed data.

n

the sample size.

conf.level

Confidence level. The default is 0.95.

details

TRUE/FALSE, can be abbreviated. To choose whether to compute the confidence interval for the whole sample points and output the infimum coverage probability. The default is FALSE.

Details

Suppose X~bino(n,p), the sample space of X is {0,1,...,n}. Wang (2014) proposed an admissible interval which is obtained by uniformly shrinking the initial 1-alpha Clopper-Pearson interval from the middle to both sides of the sample space iteratively. This interval is admissible so that any proper sub-interval of it cannot assure the confidence coefficient. This means the interval cannot be shortened anymore.

Value

A list which contains the confidence interval (CI) of the sample point and the confidence intervals (CIM) for all the points and the icp.

References

Clopper, C. J. and Pearson, E. S. (1934). The use of confidence or fiducial limits in the case of the binomial. "Biometrika" 26: 404-413.

Wang, W. (2014). An iterative construction of confidence intervals for a proportion. "Statistica Sinica" 24: 1389-1410.

Examples

WbinoCI(x=2,n=5,conf.level=0.95,details=TRUE)
WbinoCI(x=2,n=5,conf.level=0.95)