poputils (version 0.4.1)

rr3: Randomly Round A Vector of Integers to Base 3

Description

Apply the 'Random Round to Base 3' (RR3) algorithm to a vector of integers (or doubles where round(x) == x.

Usage

rr3(x)

Value

A randomly-rounded version of x.

Arguments

x

A vector of integers (in the sense that round(x) == x.) Can be an rvec.

Details

The RR3 algorithm is used by statistical agencies to confidentialize data. Under the RR3 algorithm, an integer \(n\) is randomly rounded as follows:

• If \(n\) is divisible by 3, leave it unchanged

• If dividing \(n\) by 3 leaves a remainder of 1, then round down (subtract 1) with probability 2/3, and round up (add 2) with probability 1/3.

• If dividing \(n\) by 3 leaves a remainder of 1, then round down (subtract 2) with probability 1/3, and round up (add 1) with probability 2/3.

RR3 has some nice properties:

• The randomly-rounded version of \(n\) has expected value \(n\).

• If \(n\) non-negative, then the randomly rounded version of \(n\) is non-negative.

• If \(n\) is non-positive, then the randomly rounded version of \(n\) is non-positive.

Examples

x <- c(1, 5, 2, 0, -1, 3, NA)
rr3(x)