Figure 1

(*ProbabilityN: numerical value of (2.3) with c=1 and L=0.05n with n={1,2,..,40} calulated via code 'persistenceProbability.m'.
This code will generate Figure 1 in our paper.
*)

ProbabilityN:={0.9793`,0.9722`,0.966`,0.9602`,0.9545`,0.949`,0.9436`,0.9382`,0.9329`,0.9277`,0.9224`,0.9173`,0.9121`,0.907`,0.9019`,0.8969`,0.8919`,0.8869`,0.8819`,0.877`,0.8721`,0.8672`,0.8623`,0.8575`,0.8527`,0.8479`,0.8432`,0.8385`,0.8338`,0.8291`,0.8245`,0.8198`,0.8152`,0.8107`,0.8061`,0.8016`,0.7971`,0.7927`,0.7882`,0.7838`}
ExperimentLogPro:=Table[{0.05+0.05*(n-1),Log[ProbabilityN[[n]]]},{n,1,40}]
data:=ExperimentLogPro
lm=LinearModelFit[data,x,x];Normal[lm];
T5:=ListPlot[ExperimentLogPro,PlotStyle->{Red,PointSize[0.013]}]
T4:=Plot[lm[x],{x,0.05,2},PlotStyle->{Blue,Dashed}]
Show[T5,T4]

Figure 2

(*KappaHat: numerical value of (OverHat[κ])(c) with c in {-3.5,-3,...,1.5} obtained by linear interpolation of (Log(L), P(c,L)) in (1.8), where P(c,L) is calulated via Bornemann's method.

KappaTilde: (OverTilde[κ])(c) with c in {-4,-3.95,...,1.5} obtained via formula (1.6).

This code will generate Figure 2 in our paper.
*)

KappaHat:={0.023,0.112,0.399,1.099,2.493,4.858,8.468,13.540,20.574,29.302,40.52}
KappaTilde:={53.1970,
51.7250,
50.3211,
48.9148,
47.6364,
46.3327,
44.9741,
43.7147,
42.4240,
41.2521,
40.0276,
38.7916,
37.5676,
36.5191,
35.3368,
34.3163,
33.1655,
32.1785,
31.1121,
30.0973,
29.0875,
28.1285,
27.1835,
26.2983,
25.3481,
24.4977,
23.6030,
22.7498,
21.9176,
21.1720,
20.4063,
19.6204,
18.8667,
18.1436,
17.4521,
16.7496,
16.0816,
15.4480,
14.8113,
14.1772,
13.5846,
13.0027,
12.4380,
11.8728,
11.3453,
10.8273,
10.3368,
9.8463,
9.3370,
8.8861,
8.4499,
8.0284,
7.6213,
7.2284,
6.8494,
6.4842,
6.1325,
5.7941,
5.4687,
5.1562,
4.8562,
4.5685,
4.2929,
4.0291,
3.7769,
3.5360,
3.3062,
3.0871,
2.8786,
2.6804,
2.4921,
2.3136,
2.1446,
1.9847,
1.8337,
1.6914,
1.5573,
1.4314,
1.3132,
1.2025,
1.0992,
1.0026,
0.9127,
0.8290,
0.7515,
0.6796,
0.6133,
0.5522,
0.4960,
0.4445,
0.3973,
0.3543,
0.3151,
0.2796,
0.2474,
0.2183,
0.1922,
0.1687,
0.1477,
0.1290,
0.1123,
0.0975,
0.0844,
0.0729,
0.0627,
0.0539,
0.0461,
0.0394,
0.0335,
0.0285,
0.0241}
KappaHatTable:=Table[{1.5-(n-1)0.5,KappaHat[[n]]},{n,1,11}]
kappaTildeTable:=Table[{-4+(n-1)*0.05,KappaTildeMatlab[[n]]},{n,1,Length[KappaTildeMatlab]}];
ComparisonData:=Table[{{1.5-(n-1)/2,Abs[KappaHat[[n]]-KappaTilde[[n]]]}},{n,1,11}]
f21:=ListLinePlot[kappaTildeTable,PlotStyle->Black];f22:=ListPlot[KappaHatTable,PlotStyle->Red];Show[f21,f22]