Gas PDF from three simulations with a mean density of ⟨ρ⟩ = 10³ H/cm³ (left panel) is depicted. The solid grey lines represent the data, while the dashed lines indicate the fits using Equation (15). The fitted curves are shown in different colours, representing the three turbulence levels: ℳ = 1, 3.5, and 10, displayed in purple, orange, and green, respectively. The circle marker indicates the position of t_min, while the vertical lines mark the start and end of the fit range. The right panel illustrates the relationship between the goodness of fit, measured by the χ² value, as t_min shifts from the peak to the end of the distribution.