survival.tex

Paper VI: Transfer Semigroups: Stochastic, Bayesian, Fractional, and PDE Realizations

survival.tex

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Stealth,line cap=round,line join=round]
2 \path[use as bounding box] (0,-.6) rectangle (14,4.8);
3 \draw[black!13,line width=.25pt] (0.8,0.65) -- (0.8,3.85);
4 \draw[] (0.8,0.59) -- (0.8,0.71);
5 \node[font=\small,align=center,font=\scriptsize] at (0.8,0.39) {0};
6 \draw[black!13,line width=.25pt] (2.5,0.65) -- (2.5,3.85);
7 \draw[] (2.5,0.59) -- (2.5,0.71);
8 \node[font=\small,align=center,font=\scriptsize] at (2.5,0.39) {1};
9 \draw[black!13,line width=.25pt] (4.2,0.65) -- (4.2,3.85);
10 \draw[] (4.2,0.59) -- (4.2,0.71);
11 \node[font=\small,align=center,font=\scriptsize] at (4.2,0.39) {2};
12 \draw[black!13,line width=.25pt] (5.9,0.65) -- (5.9,3.85);
13 \draw[] (5.9,0.59) -- (5.9,0.71);
14 \node[font=\small,align=center,font=\scriptsize] at (5.9,0.39) {3};
15 \draw[black!13,line width=.25pt] (7.6,0.65) -- (7.6,3.85);
16 \draw[] (7.6,0.59) -- (7.6,0.71);
17 \node[font=\small,align=center,font=\scriptsize] at (7.6,0.39) {4};
18 \draw[black!13,line width=.25pt] (9.3,0.65) -- (9.3,3.85);
19 \draw[] (9.3,0.59) -- (9.3,0.71);
20 \node[font=\small,align=center,font=\scriptsize] at (9.3,0.39) {5};
21 \draw[black!13,line width=.25pt] (0.8,0.65) -- (9.3,0.65);
22 \node[font=\small,align=center,anchor=east,font=\scriptsize] at (0.64,0.65) {0};
23 \draw[black!13,line width=.25pt] (0.8,2.25) -- (9.3,2.25);
24 \node[font=\small,align=center,anchor=east,font=\scriptsize] at (0.64,2.25) {0.5};
25 \draw[black!13,line width=.25pt] (0.8,3.85) -- (9.3,3.85);
26 \node[font=\small,align=center,anchor=east,font=\scriptsize] at (0.64,3.85) {1};
27 \draw[->,line width=.6pt] (0.8,0.65) -- (9.42,0.65);
28 \draw[->,line width=.6pt] (0.8,0.65) -- (0.8,3.97);
29 \node[font=\small,align=center,font=\scriptsize] at (5.05,0.1) {time $t$};
30 \node[font=\small,align=center,anchor=west,font=\scriptsize] at (0.8,4.25) {probability or rate};
31 \draw[line width=1.1pt] plot coordinates {(0.8,3.85) (0.885,3.846131) (0.97,3.835028) (1.055,3.817405) (1.14,3.793926) (1.225,3.765203) (1.31,3.731804) (1.395,3.694253) (1.48,3.653034) (1.565,3.608595) (1.65,3.561347) (1.735,3.511671) (1.82,3.459916) (1.905,3.406402) (1.99,3.351424) (2.075,3.295253) (2.16,3.238135) (2.245,3.180296) (2.33,3.121944) (2.415,3.063264) (2.5,3.004428) (2.585,2.945592) (2.67,2.886894) (2.755,2.828461) (2.84,2.770407) (2.925,2.712835) (3.01,2.655834) (3.095,2.599487) (3.18,2.543865) (3.265,2.489031) (3.35,2.435041) (3.435,2.381943) (3.52,2.329779) (3.605,2.278583) (3.69,2.228386) (3.775,2.179211) (3.86,2.131078) (3.945,2.084003) (4.03,2.037997) (4.115,1.993067) (4.2,1.949219) (4.285,1.906453) (4.37,1.864768) (4.455,1.82416) (4.54,1.784624) (4.625,1.746152) (4.71,1.708733) (4.795,1.672357) (4.88,1.637011) (4.965,1.602681) (5.05,1.569352) (5.135,1.537008) (5.22,1.505632) (5.305,1.475206) (5.39,1.445713) (5.475,1.417134) (5.56,1.38945) (5.645,1.362642) (5.73,1.33669) (5.815,1.311574) (5.9,1.287274) (5.985,1.263772) (6.07,1.241046) (6.155,1.219076) (6.24,1.197844) (6.325,1.177329) (6.41,1.157512) (6.495,1.138374) (6.58,1.119896) (6.665,1.102058) (6.75,1.084842) (6.835,1.068231) (6.92,1.052205) (7.005,1.036748) (7.09,1.021842) (7.175,1.00747) (7.26,0.993615) (7.345,0.980262) (7.43,0.967393) (7.515,0.954994) (7.6,0.94305) (7.685,0.931546) (7.77,0.920466) (7.855,0.909798) (7.94,0.899526) (8.025,0.889639) (8.11,0.880123) (8.195,0.870965) (8.28,0.862152) (8.365,0.853674) (8.45,0.845518) (8.535,0.837674) (8.62,0.830129) (8.705,0.822874) (8.79,0.815898) (8.875,0.809191) (8.96,0.802744) (9.045,0.796547) (9.13,0.790591) (9.215,0.784868) (9.3,0.779369)};
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34 \node[font=\small,align=center] at (11.7,3.8) {solid: survival $S(t)$};
35 \node[font=\small,align=center] at (11.7,2.8) {dashed: absorbed mass};
36 \node[font=\small,align=center] at (11.7,1.8) {dotted: hazard $h(t)$};
37 \node[font=\small,align=center,font=\scriptsize] at (11.7,0.6) {$h(0)=0$, but eventual exit\\has probability one.};
38 \end{tikzpicture}

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