Deriving the distribution of coordinate errors in displacement processes with minimum displacement distance
When dealing with data on sensitive subjects, one often encounters artificial measurement error introduced to protect confidentiality. In the field of geomasking specifically, survey units are geo-located and their coordinates randomly displaced. Measurement error models are useful to tackle this issue in an analysis, but those typically require analytical expressions for the distribution of coordinate errors for a given displacement mechanism. In a somewhat recent PhD thesis , Hossain (2023) has derived an analytical expression for the error distribution of the most basic geomask, the circular uniform random displacement mask. In this post, I build on his work to derive an analogous formula for the more recent so-called donut mask . Background The most straightforward geomask is the random displacement geomask, which has been treated in several previous posts . It draws a random angle and a random distance, both from a uniform distribution, then calculates the $x$- and $y$-of...