Table 1 Theoretical waiting time distribution for severity s
From: Waiting time distribution in public health care: empirics and theory
d | f(d∣s) | F(d∣s) | Survival Function | Hazard Function |
|---|---|---|---|---|
P(D=d∣s) | P(D ≤ d]∣ s) | P(D > d ∣ s) | P(D=d|D ≥ d,s) | |
0 | 0 | 0 | 1 | 0 |
1 | \(\frac {k_{1,s,t}}{k_{s,t}}\) | \(\frac {k_{1,s,t}}{k_{s,t}}\) | \(1-\frac {k_{1,s,t}}{k_{s,t}} \,=\, \frac {\sum _{d=2}^{q}k_{d,s,t}}{k_{s,t}}\) | \(\frac {k_{1,s,t}}{\ k_{s,t}}\) |
2 | \(\frac {k_{2,s,t}}{k_{s,t}}\) | \(\frac {k_{1,s,t}+k_{2,s,t}}{k_{s,t}}\) | \(1-\frac {k_{1,s,t}+k_{2,s,t}}{k_{s,t}} \,=\, \frac {\sum _{d=3}^{q}k_{d,s,t}}{k_{s,t}}\) | \(\frac {k_{2,s,t}}{\sum _{d=2}^{q}k_{d,s,t}}\) |
· | · | · | · | · |
· | · | · | · | · |
q−1 | \(\frac {k_{q-1,s,t}}{k_{s,t}}\) | \(\frac {\sum _{d=1}^{q-1} k_{d,s,t}}{k_{s,t}}\) | \(\frac {k_{q,s,t}}{k_{s,t}}\) | \(\frac {k_{(q-1),s,t}}{k_{(q-1),s,t}+k_{q,s,t}}\) |
q | \(\frac {k_{q,s,t}}{k_{s,t}}\) | 1 | 0 | 1 |