| WhyperCI_M {ExactCIone} | R Documentation |
An Admissible Exact Confidence Interval for M, the Number of White Balls in an Urn
Description
The confidence interval for the number of white balls in an urn that contains M white balls and N-M black balls when sampling without replacement. This function can be used to calculate the interval constructed method proposed by Wang (2015).
Usage
WhyperCI_M(x, n, N, conf.level, details = FALSE)
Arguments
x |
integer representing the number of white balls in the drawn balls. |
n |
integer representing the number of balls we draw in the urn without replacement, i.e., the sample size. |
N |
integer representing the number of all balls in an urn, i.e., the population size. |
conf.level |
the confidence level of confidence interval. |
details |
TRUE/FALSE, can be abbreviate. If choose FALSE, the confidence interval at the observed X will be returned. If choose TRUE, the confidence intervals for all sample points and the infimum coverage probability will be returned. Default is FALSE. |
Details
Suppose X~Hyper(M,N,n). When N and n are known, Wang (2015) construct an admissible confidence interval for N by uniformly shrinking the initial 1-alpha Clopper-Pearson type interval from the mid-point of the sample space to 0. 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 i) the confidence interval for M, ii)the confidence interval for p=M/N (this interval is equal to the previous interval divided by N) and iii) the infimum coverage probability of the two intervals.
References
Wang, W. (2015). Exact Optimal Confidence Intervals for Hypergeometric Parameters. "Journal of the American Statistical Association" 110 (512): 1491-1499.
Examples
WhyperCI_M(0,50,2000,0.95,details = TRUE)
WhyperCI_M(0,50,2000,0.95)