WhyperCI_N | R Documentation |
An admissible exact confidence interval for the number of balls in an urn, which is the population number of a hypergeometric distribution. This function can be used to calculate the interval constructed method proposed by Wang (2015).
WhyperCI_N(x, n, M, conf.level, details = FALSE)
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. |
M |
the number of white balls in the urn. |
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. |
Suppose X~Hyper(M,N,n). When M 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 0 to min(M,n). 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.
a list which contains i) the confidence interval for N and ii) the infimum coverage probability of the intervals.
Wang, W. (2015). Exact Optimal Confidence Intervals for Hypergeometric Parameters. "Journal of the American Statistical Association" 110 (512): 1491-1499.
WhyperCI_N(10,50,800,0.95,details=TRUE)
WhyperCI_N(50,50,800,0.95)
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