The Truncated-Uniform-Laplace (Tulap) Distribution

Distribution function and random generation for the Tulap distribution.

rtulap(n, m = 0, b = 0, q = 0)

ptulap(t, m = 0, b = 0, q = 0)

Arguments

n	number of observations
m	vector of medians
b	vector of Discrete Laplace noise parameters, obtained by \(exp(-\epsilon)\)
q	vector of truncated quantiles
t	vector of quantiles

Value

ptulap gives the distribution function and rtulap generates random derviates.

References

ptulap and rtulap are based on 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.

Examples

sample <- rtulap(1000, 1, 0.3, 0.05)
sample[1:10]
#>  [1] 0.8339134 0.6628285 0.2521001 1.2101627 1.3187668 1.8268291 0.4157301
#>  [8] 1.1775327 0.9533265 0.5523591
plot(density(sample))
ptulap(0.5, 0, 0.3, 0.05)
#> [1] 0.7834008