. 2021 Jul 14;11:14495. doi: 10.1038/s41598-021-93238-0

Table 6.

Equations for f1, f2, hazard and survival for time-only, Gaussian and Exponential spatial kernels.

	$f_{1} (t_{i} \| t_{j} ; α_{i, j})$	$f_{2} (x_{i} \| x_{j} ; β)$	Hazard	Survival
Exponential	$α (t_{i} - t_{j} - γ) e^{- \frac{1}{2} α (t_{i} - t_{j} - γ)}$	$e^{- β (x_{i} - x_{j})}$	$β α (t_{i} - t_{j} - γ) e^{- β (x_{i} - x_{j})}$	$e^{- \frac{1}{2} α (t_{i} - t_{j} - γ)} \frac{1}{β}$
Gaussian	$α (t_{i} - t_{j} - γ) e^{- \frac{1}{2} α (t_{i} - t_{j} - γ)}$	$e^{- β {(x_{i} - x_{j})}^{2}}$	$\frac{2 \sqrt{β} α (t_{i} - t_{j} - γ) e^{- β {(x_{i} - x_{j})}^{2}}}{\sqrt{π}}$	$e^{- \frac{1}{2} α (t_{i} - t_{j} - γ)} \frac{\sqrt{π}}{2 \sqrt{β}}$
Time only	$α (t_{i} - t_{j} - γ) e^{- \frac{1}{2} α (t_{i} - t_{j} - γ)}$	n/a	$α (t_{i} - t_{j} - γ)$	$e^{- \frac{1}{2} α (t_{i} - t_{j} - γ)}$