Extrapolation of lognormal CDF parameters μ and σ (Equation B.1) towards ESPEs. The best-fit values of μ and σ for given values of f₈₀₀ and their 1σ uncertainties are shown by black points with error bars in panels a and b, while panel c shows their mutual relation. Blue and green colours correspond to the fit of μ and σ as functions of f₈₀₀ performed with the MCMC approach for the offset power-law and parabolic functional forms (see Table C.1), respectively. Shaded areas correspond to 68% CrI of the fit, while the lines correspond to the median values within these CrIs. The boundary of the ESPE definition (f₈₀₀ > 10⁸ cm⁻²) is shown with the red vertical ESPE line.