Fig 2. Accuracy of approximate transformation.

We compare the accuracy of two approximate solutions to the non-linear transformation f(θ) (here, f(θ) is given by the solution to the logistic model and $\mathit{\theta }={[\lambda ,K,r_0]}^{⊺}$, see Eq (24)). In (A) θ has a multivariate normal distribution with independent components; in (B) θ has a multivariate normal distribution with correlation between λ and K; and, in (C) θ has independent, translated-gamma components such that the marginals have relatively strong skewnesses of $({\omega }_{\lambda },{\omega }_K,{\omega }_{r_0})=(1,-1,0.2)$. In all cases, we show a kernel density estimate produced from 10⁵ samples, the normal approximation (blue dashed), and the translated gamma approximation (red dashed). In the supporting material (Table A in S1 File) we provide a statistical comparison between the simulated and approximate distributions using the Kolmogorov-Smirnov test.