ddnorm {dapper}

The Discrete Gaussian Distribution

Description

The probability mass function and random number generator for the discrete Gaussian distribution with mean mu and scale parameter sigma.

Usage

ddnorm(x, mu = 0, sigma = 1, log = FALSE)

rdnorm(n, mu = 0, sigma = 1)

Arguments

x

vector of quantiles.

mu

location parameter.

sigma

scale parameter.

log

logical; if TRUE, probabilities are given as log(p).

n

number of random deviates.

Details

Probability mass function

P[X = x] = \dfrac{e^{-(x - \mu)^2/2\sigma^2}}{\sum_{y \in \mathbb{Z}} e^{-(x-\mu)^2/2\sigma^2}}.

Value

• ddnorm() returns a numeric vector representing the probability mass function of the discrete Gaussian distribution.

• rdnorm() returns a numeric vector of random samples from the discrete Gaussian distribution.

References

Canonne, C. L., Kamath, G., & Steinke, T. (2020). The Discrete Gaussian for Differential Privacy. arXiv. doi:10.48550/ARXIV.2004.00010

Examples

# mass function
ddnorm(0)

# mass function is also vectorized
ddnorm(0:10, mu = 0, sigma = 5)

# generate random samples
rdnorm(10)