  During cosmic reionization, the 21-cm brightness fluctuations were highly
non-Gaussian, and complementary statistics can be extracted from the
distribution of pixel brightness temperatures that are not derivable from the
21-cm power spectrum. One such statistic is the 21-cm difference PDF, the
probability distribution function of the difference in the 21-cm brightness
temperatures between two points, as a function of the distance between the
points. Guided by 21-cm difference PDFs extracted from simulations, we perform
a maximum likelihood analysis on mock observational data, and analyze the
ability of present and future low-frequency radio array experiments to estimate
the shape of the 21-cm difference PDF, and measure the history of cosmic
reionization. We find that one-year data with an experiment such as the
Murchison Wide-field Array should suffice for probing large scales during the
mid-to-late stages of reionization, while a second-generation experiment should
yield detailed measurements over a wide range of scales during most of the
reionization era.
