Finding Asymptotically Unbiased Two-Sided Confidence Intervals

Finding Asymptotically Unbiased Two-Sided Confidence Intervals

CITwoSide(alpha, Z, size, b, q)

Arguments

alpha	The confidence level of the returned confidence interval
Z	A Binomial sample with Tulap noise
size	The number of trials in Binomial distribution (parameter n in Binomial(n, \(\theta\)))
b	The discrete Laplace noise parameter, obtained by \(exp(-\epsilon)\)
q	The truncated quantiles

Value

An asymptotically unbiased two-sided confindence interval

References

Awan, Jordan Alexander, and Aleksandra Slavkovic. 2020. "Differentially Private Inference for Binomial Data". Journal of Privacy and Confidentiality 10 (1). https://doi.org/10.29012/jpc.725.

See also

Finding one-sided confidence intervals CILower and CIUpper

Examples

CITwoSide(alpha = 0.05, Z = 18, size = 30, b = exp(-1), q = 0.05) #(0.411, 0.767)
#> [1] 0.4107206 0.7667096