Table 2:

Models adopted to predict the distribution of MT given ID. We used the quadratic variance model with constant term (Equation 9) as an example to explain parameter derivation. Each of the variance models listed in Table 1 can be used to substitute quadratic variance model to predict MT variance of the distribution. M and V stand for the mean and variance. In truncated Gaussian, ϕ(x) and Φ(x) stands for probability density function (PDF) and cumulative distribution function (CDF).

Distribution type	Models and parameters	Predicting model parameters based on ID using quadratic variance model as an example (M: mean, V: variance)	Empirically determined parameters
Gaussian	$X~\mathcal{N}(M,\sqrt{V})$	M = a + b · ID V = c + d · ID2	a, b, c, d
Truncated Gaussian with lower bound 0	$X~\mathcal{N}(\mu ,\sigma )[0,]$ μ : location σ : scale	μ = a + b · ID σ2 = c + d · ID2 $\alpha =-\frac{\mu }{\sigma }$ $\varphi (\alpha ):\text{\hspace{0.17em}PDF},\varphi (\alpha )=\frac{1}{\sqrt{2\cdot \pi }}\cdot \text{exp}\left(-\frac{1}{2}\cdot {\alpha }^2\right)$ $\Phi (\alpha ):\text{\hspace{0.17em}CDF},\Phi (\alpha )=\frac{1}{2}\cdot \left(1+\text{erf}\left(\frac{\alpha }{\sqrt{2}}\right)\right)$ Z = 1 – Φ(α) $M=\mu +\sigma \cdot \frac{\varphi (\alpha )}{Z}$ $V={\sigma }^2\cdot \left(1+\alpha \cdot \frac{\varphi (\alpha )}{Z}-{\left(\frac{\varphi (\alpha )}{Z}\right)}^2\right)$	a, b, c, d
Lognormal	X ~ Lognormal(μ, σ) μ : location σ : scale	M = a + b · ID V = c + d · ID 2 $\mu =\text{ln}\left(\frac{M^2}{\sqrt{M^2+V}}\right)$ $\sigma =\sqrt{ln\left(1+\frac{V}{M^2}\right)}$	a, b, c, d
Gamma	X ~ Γ(α, β) α : shape β : inverse scale	M = a + b · ID V = c + d · ID2 $\alpha =\frac{M^2}{V}$ $\beta =\frac{M}{V}$	a, b, c, d
Extreme value	X ~ Gumbel(μ, β) μ : location β : scale	M = a + b · ID V = c + d · ID2 μ = M – β · γ γ : Euler-Mascheroni constant	a, b, c, d
ExGaussian	X ~ EMG(μ, σ, λ) μ : location σ : scale λ : shape	M = a + b · ID V = c + d · ID2 $\mu =M-\frac{1}{\lambda }$ $\sigma =\sqrt{V-\frac{1}{{\lambda }^2}}$ $\lambda =\frac{k}{ID}$ [11]	a, b, c, d, k