  One-point probability distribution functions (PDFs) of the cosmic matter
density are powerful cosmological probes that extract non-Gaussian properties
of the matter distribution and complement two-point statistics. Computing the
covariance of one-point PDFs is key for building a robust galaxy survey
analysis for upcoming surveys like Euclid and the Rubin Observatory LSST and
requires good models for the two-point PDFs characterising spatial
correlations. In this work, we obtain accurate PDF covariances using effective
shifted lognormal two-point PDF models for the mildly non-Gaussian weak lensing
convergence and validate our predictions against large sets of Gaussian and
non-Gaussian maps. We show how the dominant effects in the covariance matrix
capturing super-sample covariance arise from a large-separation expansion of
the two-point PDF and discuss differences between the covariances obtained from
small patches and full sky maps. Finally, we describe how our formalism can be
extended to characterise the PDF covariance for 3D-dimensional spectroscopic
fields using the 3D matter PDF as an example. We describe how covariances from
simulated boxes with fixed overall density can be supplemented with the missing
super-sample covariance effect by relying on theoretical predictions validated
against separate-universe style simulations.
