Finding One-Sided Confidence Intervals

Finding One-Sided Confidence Intervals

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

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

Arguments

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

Value

`CILower` returns a lower bound while `CIUpper` returns an upper bound.

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 asymptotically unbiased two-sided confidence intervals CITwoSide

Examples

CILower(0.05, 7, 10, exp(-1), 0.05) #confidence interval (0.384, 1)
#> [1] 0.3844819
CIUpper(0.05, 2, 10, exp(-1), 0.05) #confidence interval (0, 0.517)
#> [1] 0.517379