  We explore error distributions in Epoch of Reionization 21-cm power spectrum
estimators using a combination of mathematical analysis and numerical
simulations. We provide closed form solutions for the error distributions of
individual bins in 3d-power spectra for two estimators currently in use in the
field, which we designate as ``straight-square" and ``cross-multiply"
estimators. We then demonstrate when the corresponding spherically binned power
spectra should (and should not) have Gaussian error distributions, which
requires appealing to nonstandard statements of the central limit theorem. This
has important implications for how upper limits are reported, as well as how
cosmological inferences are performed based on power spectrum measurements.
Specifically, assuming a Gaussian error distribution can over or underestimate
the upper limit depending on the type of estimator, and produces overly compact
likelihood functions for the power spectrum.
