Probability density function of the population fractions (H I, Ca II, and Mg II) as a function of temperature. The panels in the upper row are a zoomed-in view of part of the panels in the lower row for the temperature range of T <  30 kK. Colored lines show the results from the recipe of CL12 (red), the coronal approximation with a two-level atom (blue), the Saha equation with a constant n_e = 10¹³ cm⁻³ (green), and the adopted fit of the PDF (yellow).