The early epoch in which the first stars and galaxies formed is among the most exciting unexplored eras of the Universe. A major research effort focuses on probing this era with the 21-cm spectral line of hydrogen. While most research focused on statistics like the 21-cm power spectrum or the sky-averaged global signal, there are other ways to analyze tomographic 21-cm maps, which may lead to novel insights. We suggest statistics based on quantiles as a method to probe non-Gaussianities of the 21-cm signal. We show that they can be used in particular to probe the variance, skewness, and kurtosis of the temperature distribution, but are more flexible and robust than these standard statistics. We test these statistics on a range of possible astrophysical models, including different galactic halo masses, star-formation efficiencies, and spectra of the X-ray heating sources, plus an exotic model with an excess early radio background. Simulating data with angular resolution and thermal noise as expected for the Square Kilometre Array (SKA), we conclude that these statistics can be measured out to redshifts above 20 and offer a promising statistical method for probing early cosmic history.
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