ddnorm: The Discrete Gaussian Distribution

In dapper: Data Augmentation for Private Posterior Estimation

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, log unnormalized probabilities are returned.
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. \Sexpr[results=rd]{tools:::Rd_expr_doi("https://doi.org/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)

dapper documentation built on Oct. 29, 2024, 9:06 a.m.