The function simSC() generates simulated recurrent event data from either a Cox-type model, an accelerated mean model, an accelerated rate model, or a scale-change model.

simSC(
n,
a1 = a2,
b1 = b2,
a2 = a1,
b2 = b1,
type = "cox",
zVar = 0.25,
tau = 60,
origin = 0,
summary = FALSE
)

## Arguments

n number of observation. are numeric vectors of length 2. These correspond to the $$\alpha$$, $$\beta$$, $$\eta$$, and $$\theta$$ in the joint model. See Details is a character string specifying the underlying model. The rate function type and the hazard function type are separated by a vertical bar "|", with the rate function on the left. For example, type = "cox|am" generates the recurrent process from a Cox model and the terminal event from an accelerated mean model. Setting type = "cox" gives type = "cox|cox". a numeric variable specifying the variance of the fraility variable,$$Z$$, when zVar > 0. When zVar = 0, $$Z$$ is set to a fixed constant 1. The default value is 0.25. a numeric value specifying the maximum observation time. a numeric value specifying the time origin. a logical value indicating whether a brief data summary will be printed.

## Details

The function simSC() generates simulated recurrent event data over the interval $$(0, \tau)$$ based on the specification of the recurrent process and the terminal events. Specifically, the rate function, $$\lambda(t)$$, of the recurrent process can be specified as one of the following model: $$\lambda(t) = Z \lambda_0(te^{X^\top\alpha}) e^{X^\top\beta}, h(t) = Z h_0(te^{X^\top\eta})e^{X^\top\theta},$$ where $$\lambda_0(t)$$ is the baseline rate function, $$h_0(t)$$ is the baseline hazard function, $$X$$ is a $$n$$ by $$p$$ covariate matrix and $$\alpha$$, $$Z$$ is an unobserved shared frailty variable, and $$(\alpha, \eta)$$ and $$(\beta, \theta)$$ correspond to the shape and size parameters of the rate function and the hazard function, respectively.

For all scenarios, two covariates are considered; $$X = (X_1, X_2)$$, where $$X_1$$ follows a Bernoulli distribution with probability 0.5 and $$X_2$$ follows a standard normal distribution. The censoring time could be either independent (given covariates) or informative. The simulated data is used for illustration. An informative censoring time, $$C$$, is generated separately from an exponential distribution with a rate parameter of 1 / 60 if $$X_1$$ is 1, or $$Z^2 / 30$$ if $$X_1$$ is 0. The observed recurrent events is then observed up to the minimum of $$C$$, terminal event, and $$\tau$$. Lastly, we assume the baseline functions $$\lambda_0(t) = \frac{2}{1 + t}, h_0(t) = \frac{1}{8(1 + t)}.$$

reReg

## Examples

set.seed(123)
simSC(100, c(-1, 1), c(-1, 1), summary = TRUE)#>
#> Summary results for number of recurrent event per subject:
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
#>    0.00    1.00    2.00    4.29    6.00   34.00
#>
#> Number of failures: 24 (24%); Number of censored events: 76 (76%)
#>
#> Number of x1 == 1: 41 (41%); Number of x1 == 0: 59 (59%)
#> Summary results for x2:
#>     Min.  1st Qu.   Median     Mean  3rd Qu.     Max.
#> -3.31068 -0.82464 -0.03736 -0.01454  0.73703  2.70817
#>
#> #>      id      t.start       t.stop event status x1           x2
#> 1     1  0.000000000 44.426167910     1      0  1  0.314152900
#> 2     1 44.426167910 60.000000000     0      0  1  0.314152900
#> 3     2  0.000000000  0.094921034     1      0  0  1.844838671
#> 4     2  0.094921034  0.125154110     1      0  0  1.844838671
#> 5     2  0.125154110  0.128363300     1      0  0  1.844838671
#> 6     2  0.128363300  0.128893639     1      0  0  1.844838671
#> 7     2  0.128893639  0.151798159     1      0  0  1.844838671
#> 8     2  0.151798159  0.156259693     1      0  0  1.844838671
#> 9     2  0.156259693  0.162467082     1      0  0  1.844838671
#> 10    2  0.162467082  0.192499996     1      0  0  1.844838671
#> 11    2  0.192499996  0.205361520     1      0  0  1.844838671
#> 12    2  0.205361520  0.212755086     0      1  0  1.844838671
#> 13    3  0.000000000 60.000000000     0      0  1 -0.981917149
#> 14    4  0.000000000  0.056292351     1      0  1  2.196003763
#> 15    4  0.056292351  0.072279983     1      0  1  2.196003763
#> 16    4  0.072279983  0.185730262     1      0  1  2.196003763
#> 17    4  0.185730262  0.289228289     1      0  1  2.196003763
#> 18    4  0.289228289  1.361980416     1      0  1  2.196003763
#> 19    4  1.361980416  1.874695287     1      0  1  2.196003763
#> 20    4  1.874695287  3.977850859     1      0  1  2.196003763
#> 21    4  3.977850859  4.480471395     1      0  1  2.196003763
#> 22    4  4.480471395  4.823564663     1      0  1  2.196003763
#> 23    4  4.823564663  4.982837852     1      0  1  2.196003763
#> 24    4  4.982837852  5.317014620     1      0  1  2.196003763
#> 25    4  5.317014620  5.340135942     1      0  1  2.196003763
#> 26    4  5.340135942  5.901524918     1      0  1  2.196003763
#> 27    4  5.901524918  5.956915706     1      0  1  2.196003763
#> 28    4  5.956915706  8.325919518     0      0  1  2.196003763
#> 29    5  0.000000000  0.129123255     1      0  0 -0.204667665
#> 30    5  0.129123255  0.693168398     1      0  0 -0.204667665
#> 31    5  0.693168398  1.332298107     1      0  0 -0.204667665
#> 32    5  1.332298107  1.858225226     1      0  0 -0.204667665
#> 33    5  1.858225226  3.180539355     0      0  0 -0.204667665
#> 34    6  0.000000000  0.216686503     1      0  0  0.975142936
#> 35    6  0.216686503  0.319404774     1      0  0  0.975142936
#> 36    6  0.319404774  0.588142311     1      0  0  0.975142936
#> 37    6  0.588142311  0.618091546     1      0  0  0.975142936
#> 38    6  0.618091546  1.085061481     1      0  0  0.975142936
#> 39    6  1.085061481  1.298248152     1      0  0  0.975142936
#> 40    6  1.298248152  1.354466114     1      0  0  0.975142936
#> 41    6  1.354466114  1.433272512     1      0  0  0.975142936
#> 42    6  1.433272512  1.479426384     1      0  0  0.975142936
#> 43    6  1.479426384  1.486390825     1      0  0  0.975142936
#> 44    6  1.486390825  1.603648039     1      0  0  0.975142936
#> 45    6  1.603648039  3.036196533     1      0  0  0.975142936
#> 46    6  3.036196533  4.378587285     1      0  0  0.975142936
#> 47    6  4.378587285  5.733083522     1      0  0  0.975142936
#> 48    6  5.733083522  7.070218220     1      0  0  0.975142936
#> 49    6  7.070218220  8.161021327     0      0  0  0.975142936
#> 50    7  0.000000000 12.204839610     0      0  0 -0.867566116
#> 51    8  0.000000000  0.480456759     1      0  0 -0.501187592
#> 52    8  0.480456759  9.182117175     0      0  0 -0.501187592
#> 53    9  0.000000000  0.004517227     1      0  0  0.785591163
#> 54    9  0.004517227  0.010845527     1      0  0  0.785591163
#> 55    9  0.010845527  0.231110693     1      0  0  0.785591163
#> 56    9  0.231110693  0.428345024     1      0  0  0.785591163
#> 57    9  0.428345024  0.481381589     1      0  0  0.785591163
#> 58    9  0.481381589  0.850984615     1      0  0  0.785591163
#> 59    9  0.850984615  0.957997791     1      0  0  0.785591163
#> 60    9  0.957997791  1.796847636     1      0  0  0.785591163
#> 61    9  1.796847636  2.040113204     1      0  0  0.785591163
#> 62    9  2.040113204  3.912920907     1      0  0  0.785591163
#> 63    9  3.912920907  4.187313729     0      1  0  0.785591163
#> 64   10  0.000000000 60.000000000     0      0  1 -2.102247324
#> 65   11  0.000000000  0.493291422     1      0  0 -0.042204930
#> 66   11  0.493291422  0.716490115     1      0  0 -0.042204930
#> 67   11  0.716490115  0.720544178     1      0  0 -0.042204930
#> 68   11  0.720544178  2.348637230     1      0  0 -0.042204930
#> 69   11  2.348637230  3.635269917     0      0  0 -0.042204930
#> 70   12  0.000000000  0.747892583     1      0  1 -0.404809413
#> 71   12  0.747892583  1.156108466     1      0  1 -0.404809413
#> 72   12  1.156108466 18.031380046     0      0  1 -0.404809413
#> 73   13  0.000000000 18.452001885     0      0  1 -0.112765966
#> 74   14  0.000000000  0.113047048     1      0  1  1.797140441
#> 75   14  0.113047048  0.136108410     1      0  1  1.797140441
#> 76   14  0.136108410  0.365452359     1      0  1  1.797140441
#> 77   14  0.365452359  0.391098229     1      0  1  1.797140441
#> 78   14  0.391098229  0.527733393     1      0  1  1.797140441
#> 79   14  0.527733393  0.590708249     1      0  1  1.797140441
#> 80   14  0.590708249  0.902421315     1      0  1  1.797140441
#> 81   14  0.902421315  1.019193212     1      0  1  1.797140441
#> 82   14  1.019193212  1.787599159     1      0  1  1.797140441
#> 83   14  1.787599159  2.533196580     1      0  1  1.797140441
#> 84   14  2.533196580  2.703503861     1      0  1  1.797140441
#> 85   14  2.703503861  3.003116132     1      0  1  1.797140441
#> 86   14  3.003116132  3.533033566     1      0  1  1.797140441
#> 87   14  3.533033566  5.135138577     1      0  1  1.797140441
#> 88   14  5.135138577  6.001520455     1      0  1  1.797140441
#> 89   14  6.001520455  8.129608877     1      0  1  1.797140441
#> 90   14  8.129608877  8.147785928     1      0  1  1.797140441
#> 91   14  8.147785928 14.463682858     1      0  1  1.797140441
#> 92   14 14.463682858 15.714660929     1      0  1  1.797140441
#> 93   14 15.714660929 16.000543655     1      0  1  1.797140441
#> 94   14 16.000543655 16.698048789     1      0  1  1.797140441
#> 95   14 16.698048789 19.074894239     1      0  1  1.797140441
#> 96   14 19.074894239 20.816736023     1      0  1  1.797140441
#> 97   14 20.816736023 21.072708316     0      1  1  1.797140441
#> 98   15  0.000000000  1.995573195     1      0  0 -0.810326258
#> 99   15  1.995573195  4.124126960     1      0  0 -0.810326258
#> 100  15  4.124126960 10.801766722     1      0  0 -0.810326258
#> 101  15 10.801766722 11.024803256     0      0  0 -0.810326258
#> 102  16  0.000000000  0.234114367     1      0  1  1.900900074
#> 103  16  0.234114367  0.851754751     1      0  1  1.900900074
#> 104  16  0.851754751  1.606035952     1      0  1  1.900900074
#> 105  16  1.606035952  1.762289385     1      0  1  1.900900074
#> 106  16  1.762289385  1.826441917     1      0  1  1.900900074
#> 107  16  1.826441917  3.124673952     1      0  1  1.900900074
#> 108  16  3.124673952  3.243853424     1      0  1  1.900900074
#> 109  16  3.243853424  4.395090357     1      0  1  1.900900074
#> 110  16  4.395090357  4.992642076     1      0  1  1.900900074
#> 111  16  4.992642076  5.642810119     0      0  1  1.900900074
#> 112  17  0.000000000  1.327927087     1      0  0  0.708954440
#> 113  17  1.327927087  2.701109679     1      0  0  0.708954440
#> 114  17  2.701109679 20.995077410     1      0  0  0.708954440
#> 115  17 20.995077410 25.360391444     1      0  0  0.708954440
#> 116  17 25.360391444 25.797039543     0      0  0  0.708954440
#> 117  18  0.000000000  0.367863189     1      0  1  0.736194775
#> 118  18  0.367863189  1.671345267     1      0  1  0.736194775
#> 119  18  1.671345267  2.488031575     1      0  1  0.736194775
#> 120  18  2.488031575 10.495364042     0      0  1  0.736194775
#> 121  19  0.000000000  0.003664993     0      1  0  1.365776554
#> 122  20  0.000000000  1.659010263     1      0  0 -0.576263893
#> 123  20  1.659010263  8.270060779     1      0  0 -0.576263893
#> 124  20  8.270060779 57.861444747     0      0  0 -0.576263893
#> 125  21  0.000000000  5.085302762     1      0  0 -0.804732320
#> 126  21  5.085302762  8.368098177     1      0  0 -0.804732320
#> 127  21  8.368098177 60.000000000     0      0  0 -0.804732320
#> 128  22  0.000000000  1.229565771     1      0  0 -0.535065812
#> 129  22  1.229565771  4.557610284     1      0  0 -0.535065812
#> 130  22  4.557610284  8.449352122     1      0  0 -0.535065812
#> 131  22  8.449352122 23.274458489     0      0  0 -0.535065812
#> 132  23  0.000000000  6.281136752     1      0  0  0.791547909
#> 133  23  6.281136752 13.303086271     1      0  0  0.791547909
#> 134  23 13.303086271 35.697385624     1      0  0  0.791547909
#> 135  23 35.697385624 60.000000000     0      0  0  0.791547909
#> 136  24  0.000000000  2.452900450     0      1  0 -0.707607151
#> 137  25  0.000000000  6.293977611     0      0  1 -1.275543372
#> 138  26  0.000000000  0.045506337     1      0  0  2.375464461
#> 139  26  0.045506337  0.178439471     1      0  0  2.375464461
#> 140  26  0.178439471  0.229764689     1      0  0  2.375464461
#> 141  26  0.229764689  0.391617573     1      0  0  2.375464461
#> 142  26  0.391617573  0.433009312     1      0  0  2.375464461
#> 143  26  0.433009312  0.444372840     1      0  0  2.375464461
#> 144  26  0.444372840  0.494782288     1      0  0  2.375464461
#> 145  26  0.494782288  0.534103344     1      0  0  2.375464461
#> 146  26  0.534103344  0.709791714     1      0  0  2.375464461
#> 147  26  0.709791714  0.715533114     1      0  0  2.375464461
#> 148  26  0.715533114  0.734933214     1      0  0  2.375464461
#> 149  26  0.734933214  0.780807122     1      0  0  2.375464461
#> 150  26  0.780807122  1.022881411     1      0  0  2.375464461
#> 151  26  1.022881411  1.099555227     1      0  0  2.375464461
#> 152  26  1.099555227  1.210136244     1      0  0  2.375464461
#> 153  26  1.210136244  1.416993677     1      0  0  2.375464461
#> 154  26  1.416993677  1.435961365     1      0  0  2.375464461
#> 155  26  1.435961365  1.730702372     1      0  0  2.375464461
#> 156  26  1.730702372  2.048041744     1      0  0  2.375464461
#> 157  26  2.048041744  2.124960370     1      0  0  2.375464461
#> 158  26  2.124960370  2.298323196     1      0  0  2.375464461
#> 159  26  2.298323196  2.591394978     1      0  0  2.375464461
#> 160  26  2.591394978  3.301813924     1      0  0  2.375464461
#> 161  26  3.301813924  3.947651924     1      0  0  2.375464461
#> 162  26  3.947651924  4.131293060     1      0  0  2.375464461
#> 163  26  4.131293060  4.251416452     1      0  0  2.375464461
#> 164  26  4.251416452  4.292132687     1      0  0  2.375464461
#> 165  26  4.292132687  4.427350682     1      0  0  2.375464461
#> 166  26  4.427350682  4.585815077     1      0  0  2.375464461
#> 167  26  4.585815077  4.987689301     1      0  0  2.375464461
#> 168  26  4.987689301  5.283218406     1      0  0  2.375464461
#> 169  26  5.283218406  5.305954276     1      0  0  2.375464461
#> 170  26  5.305954276  5.574535236     1      0  0  2.375464461
#> 171  26  5.574535236  5.827979402     1      0  0  2.375464461
#> 172  26  5.827979402  6.318148700     0      1  0  2.375464461
#> 173  27  0.000000000  2.527861668     0      0  1 -1.093589748
#> 174  28  0.000000000  0.051920460     1      0  0  0.192441582
#> 175  28  0.051920460  0.144681734     1      0  0  0.192441582
#> 176  28  0.144681734  0.247917295     1      0  0  0.192441582
#> 177  28  0.247917295  0.750263763     1      0  0  0.192441582
#> 178  28  0.750263763  1.221031857     0      0  0  0.192441582
#> 179  29  0.000000000  0.226611928     1      0  0 -0.126160381
#> 180  29  0.226611928  0.377627929     0      0  0 -0.126160381
#> 181  30  0.000000000 43.694549172     0      0  0 -1.388432140
#> 182  31  0.000000000  0.045878423     1      0  0  0.469902192
#> 183  31  0.045878423  0.512235913     1      0  0  0.469902192
#> 184  31  0.512235913  0.646405086     0      0  0  0.469902192
#> 185  32  0.000000000  1.760455139     1      0  1  0.960382357
#> 186  32  1.760455139 22.378842132     0      0  1  0.960382357
#> 187  33  0.000000000  0.951569404     1      0  1 -0.005141288
#> 188  33  0.951569404  7.505540052     1      0  1 -0.005141288
#> 189  33  7.505540052 60.000000000     0      0  1 -0.005141288
#> 190  34  0.000000000  0.515407932     1      0  0 -0.870464442
#> 191  34  0.515407932  0.896151084     1      0  0 -0.870464442
#> 192  34  0.896151084  0.931286070     0      1  0 -0.870464442
#> 193  35  0.000000000  0.944737736     1      0  0 -0.462879040
#> 194  35  0.944737736  6.428637348     1      0  0 -0.462879040
#> 195  35  6.428637348  7.544621338     1      0  0 -0.462879040
#> 196  35  7.544621338 19.917613942     0      0  0 -0.462879040
#> 197  36  0.000000000 60.000000000     0      0  0 -1.911151255
#> 198  37  0.000000000  0.367580507     1      0  1  0.369816044
#> 199  37  0.367580507  0.484168162     1      0  1  0.369816044
#> 200  37  0.484168162  3.400619282     1      0  1  0.369816044
#> 201  37  3.400619282  6.287594223     1      0  1  0.369816044
#> 202  37  6.287594223  9.211417503     1      0  1  0.369816044
#> 203  37  9.211417503 11.041441969     1      0  1  0.369816044
#> 204  37 11.041441969 60.000000000     0      0  1  0.369816044
#> 205  38  0.000000000 60.000000000     0      0  1 -0.462288057
#> 206  39  0.000000000  8.910640641     1      0  1  0.321955892
#> 207  39  8.910640641  9.839924491     1      0  1  0.321955892
#> 208  39  9.839924491 15.569450855     0      0  1  0.321955892
#> 209  40  0.000000000  0.389491429     1      0  0 -0.284001390
#> 210  40  0.389491429  1.121575864     1      0  0 -0.284001390
#> 211  40  1.121575864  3.341656791     1      0  0 -0.284001390
#> 212  40  3.341656791  6.553368190     1      0  0 -0.284001390
#> 213  40  6.553368190  7.197774398     1      0  0 -0.284001390
#> 214  40  7.197774398 29.655227938     1      0  0 -0.284001390
#> 215  40 29.655227938 31.327400120     1      0  0 -0.284001390
#> 216  40 31.327400120 60.000000000     0      0  0 -0.284001390
#> 217  41  0.000000000  0.380419607     1      0  1  1.091856443
#> 218  41  0.380419607  2.947484754     1      0  1  1.091856443
#> 219  41  2.947484754  3.485678620     1      0  1  1.091856443
#> 220  41  3.485678620 12.721763638     0      1  1  1.091856443
#> 221  42  0.000000000  2.647586860     1      0  0  0.160216363
#> 222  42  2.647586860  4.222113713     1      0  0  0.160216363
#> 223  42  4.222113713 11.930325739     0      0  0  0.160216363
#> 224  43  0.000000000  0.060869045     1      0  0  2.708168284
#> 225  43  0.060869045  0.141328881     1      0  0  2.708168284
#> 226  43  0.141328881  0.156319137     1      0  0  2.708168284
#> 227  43  0.156319137  0.283256048     1      0  0  2.708168284
#> 228  43  0.283256048  0.374894071     1      0  0  2.708168284
#> 229  43  0.374894071  0.632541474     1      0  0  2.708168284
#> 230  43  0.632541474  0.754572416     1      0  0  2.708168284
#> 231  43  0.754572416  0.787107817     1      0  0  2.708168284
#> 232  43  0.787107817  0.907544674     1      0  0  2.708168284
#> 233  43  0.907544674  0.927490095     1      0  0  2.708168284
#> 234  43  0.927490095  1.062092047     0      1  0  2.708168284
#> 235  44  0.000000000  9.902336551     1      0  0  0.286289929
#> 236  44  9.902336551 10.162711700     0      0  0  0.286289929
#> 237  45  0.000000000  1.130904205     1      0  0 -0.032510251
#> 238  45  1.130904205  1.184472075     1      0  0 -0.032510251
#> 239  45  1.184472075  1.555413216     1      0  0 -0.032510251
#> 240  45  1.555413216 60.000000000     0      0  0 -0.032510251
#> 241  46  0.000000000  7.260021570     1      0  0 -0.989678019
#> 242  46  7.260021570  7.935806037     1      0  0 -0.989678019
#> 243  46  7.935806037 10.324601177     1      0  0 -0.989678019
#> 244  46 10.324601177 37.580687785     0      0  0 -0.989678019
#> 245  47  0.000000000  4.021075863     1      0  1  0.211809928
#> 246  47  4.021075863  6.647520104     1      0  1  0.211809928
#> 247  47  6.647520104 60.000000000     0      0  1  0.211809928
#> 248  48  0.000000000  2.798082020     1      0  1 -0.972017534
#> 249  48  2.798082020  4.302783453     1      0  1 -0.972017534
#> 250  48  4.302783453 60.000000000     0      0  1 -0.972017534
#> 251  49  0.000000000  0.176975346     1      0  1  0.549224014
#> 252  49  0.176975346  0.743075179     1      0  1  0.549224014
#> 253  49  0.743075179  0.813259869     1      0  1  0.549224014
#> 254  49  0.813259869  1.153431976     1      0  1  0.549224014
#> 255  49  1.153431976  1.354066606     1      0  1  0.549224014
#> 256  49  1.354066606  2.304182033     1      0  1  0.549224014
#> 257  49  2.304182033  4.215737676     1      0  1  0.549224014
#> 258  49  4.215737676  9.764389491     1      0  1  0.549224014
#> 259  49  9.764389491 11.533429121     1      0  1  0.549224014
#> 260  49 11.533429121 12.113327177     1      0  1  0.549224014
#> 261  49 12.113327177 16.493736204     1      0  1  0.549224014
#> 262  49 16.493736204 19.744157497     1      0  1  0.549224014
#> 263  49 19.744157497 20.497090013     1      0  1  0.549224014
#> 264  49 20.497090013 30.745422361     1      0  1  0.549224014
#> 265  49 30.745422361 31.091008194     1      0  1  0.549224014
#> 266  49 31.091008194 34.601702514     0      1  1  0.549224014
#> 267  50  0.000000000  0.230084990     1      0  0 -1.049021530
#> 268  50  0.230084990 48.263490207     0      0  0 -1.049021530
#> 269  51  0.000000000  0.067797362     1      0  0  0.449133935
#> 270  51  0.067797362  0.264214934     1      0  0  0.449133935
#> 271  51  0.264214934  0.462465771     1      0  0  0.449133935
#> 272  51  0.462465771  0.806881110     1      0  0  0.449133935
#> 273  51  0.806881110  0.886435166     1      0  0  0.449133935
#> 274  51  0.886435166  5.881111896     1      0  0  0.449133935
#> 275  51  5.881111896  8.606163806     1      0  0  0.449133935
#> 276  51  8.606163806  8.942277607     1      0  0  0.449133935
#> 277  51  8.942277607 14.864964116     0      0  0  0.449133935
#> 278  52  0.000000000 13.784086765     1      0  1 -0.385855653
#> 279  52 13.784086765 27.970609279     1      0  1 -0.385855653
#> 280  52 27.970609279 41.380154919     0      0  1 -0.385855653
#> 281  53  0.000000000 45.917339621     0      0  1 -1.570135523
#> 282  54  0.000000000  0.132881709     1      0  0  1.226942601
#> 283  54  0.132881709  0.220699343     1      0  0  1.226942601
#> 284  54  0.220699343  0.428962098     1      0  0  1.226942601
#> 285  54  0.428962098  0.517601886     1      0  0  1.226942601
#> 286  54  0.517601886  0.638980442     1      0  0  1.226942601
#> 287  54  0.638980442  0.656049954     1      0  0  1.226942601
#> 288  54  0.656049954  1.253642173     1      0  0  1.226942601
#> 289  54  1.253642173  1.407435662     1      0  0  1.226942601
#> 290  54  1.407435662  1.694336288     1      0  0  1.226942601
#> 291  54  1.694336288  1.767217579     1      0  0  1.226942601
#> 292  54  1.767217579  2.159906265     1      0  0  1.226942601
#> 293  54  2.159906265  2.408250542     1      0  0  1.226942601
#> 294  54  2.408250542  2.417505832     1      0  0  1.226942601
#> 295  54  2.417505832  2.796181193     1      0  0  1.226942601
#> 296  54  2.796181193  2.863436992     1      0  0  1.226942601
#> 297  54  2.863436992  2.962453010     1      0  0  1.226942601
#> 298  54  2.962453010  3.324677789     1      0  0  1.226942601
#> 299  54  3.324677789  3.562060613     1      0  0  1.226942601
#> 300  54  3.562060613  3.913280487     1      0  0  1.226942601
#> 301  54  3.913280487  3.950248888     1      0  0  1.226942601
#> 302  54  3.950248888  4.455959171     1      0  0  1.226942601
#> 303  54  4.455959171  4.989831279     1      0  0  1.226942601
#> 304  54  4.989831279  5.192937332     1      0  0  1.226942601
#> 305  54  5.192937332  5.329145827     1      0  0  1.226942601
#> 306  54  5.329145827  5.378969353     1      0  0  1.226942601
#> 307  54  5.378969353  5.514449219     1      0  0  1.226942601
#> 308  54  5.514449219  9.091785237     1      0  0  1.226942601
#> 309  54  9.091785237 16.474294053     1      0  0  1.226942601
#> 310  54 16.474294053 19.403666424     1      0  0  1.226942601
#> 311  54 19.403666424 30.590409252     1      0  0  1.226942601
#> 312  54 30.590409252 30.962417132     0      0  0  1.226942601
#> 313  55  0.000000000  0.317940276     1      0  1  0.666694396
#> 314  55  0.317940276  1.168614638     1      0  1  0.666694396
#> 315  55  1.168614638  1.713942123     1      0  1  0.666694396
#> 316  55  1.713942123  2.607341604     1      0  1  0.666694396
#> 317  55  2.607341604  5.271562205     1      0  1  0.666694396
#> 318  55  5.271562205  5.639152530     1      0  1  0.666694396
#> 319  55  5.639152530 10.220013936     1      0  1  0.666694396
#> 320  55 10.220013936 19.553747046     1      0  1  0.666694396
#> 321  55 19.553747046 28.152110925     1      0  1  0.666694396
#> 322  55 28.152110925 38.274645992     0      0  1  0.666694396
#> 323  56  0.000000000 22.337666746     1      0  0 -1.151603163
#> 324  56 22.337666746 39.205379870     1      0  0 -1.151603163
#> 325  56 39.205379870 60.000000000     0      0  0 -1.151603163
#> 326  57  0.000000000  1.123956508     1      0  0 -0.160788483
#> 327  57  1.123956508  7.478829245     1      0  0 -0.160788483
#> 328  57  7.478829245  7.608661820     1      0  0 -0.160788483
#> 329  57  7.608661820 22.129391233     0      0  0 -0.160788483
#> 330  58  0.000000000 35.858826935     0      0  1 -0.972913776
#> 331  59  0.000000000  0.106334237     1      0  0 -0.610461659
#> 332  59  0.106334237  0.143066590     1      0  0 -0.610461659
#> 333  59  0.143066590  0.399736278     1      0  0 -0.610461659
#> 334  59  0.399736278  1.329412686     0      0  0 -0.610461659
#> 335  60  0.000000000  0.289244137     1      0  0  0.499276876
#> 336  60  0.289244137  1.119889409     1      0  0  0.499276876
#> 337  60  1.119889409  1.861822395     1      0  0  0.499276876
#> 338  60  1.861822395  1.921929449     1      0  0  0.499276876
#> 339  60  1.921929449  2.411083779     1      0  0  0.499276876
#> 340  60  2.411083779  2.546129412     1      0  0  0.499276876
#> 341  60  2.546129412  5.750243466     1      0  0  0.499276876
#> 342  60  5.750243466  6.923099549     1      0  0  0.499276876
#> 343  60  6.923099549  7.432479386     1      0  0  0.499276876
#> 344  60  7.432479386  9.919762625     0      0  0  0.499276876
#> 345  61  0.000000000  0.329834180     1      0  0  0.879364139
#> 346  61  0.329834180  1.287722228     1      0  0  0.879364139
#> 347  61  1.287722228  1.659425957     1      0  0  0.879364139
#> 348  61  1.659425957  1.756849354     1      0  0  0.879364139
#> 349  61  1.756849354  4.536289698     1      0  0  0.879364139
#> 350  61  4.536289698  7.866204392     1      0  0  0.879364139
#> 351  61  7.866204392 11.104906100     1      0  0  0.879364139
#> 352  61 11.104906100 15.570550002     1      0  0  0.879364139
#> 353  61 15.570550002 30.687902796     1      0  0  0.879364139
#> 354  61 30.687902796 58.924853849     1      0  0  0.879364139
#> 355  61 58.924853849 60.000000000     0      0  0  0.879364139
#> 356  62  0.000000000  0.423540384     1      0  1  0.923129239
#> 357  62  0.423540384  5.744994749     1      0  1  0.923129239
#> 358  62  5.744994749  7.426180952     1      0  1  0.923129239
#> 359  62  7.426180952 60.000000000     0      0  1  0.923129239
#> 360  63  0.000000000  0.233545879     1      0  0  0.693133972
#> 361  63  0.233545879  0.234017989     1      0  0  0.693133972
#> 362  63  0.234017989  0.538450199     1      0  0  0.693133972
#> 363  63  0.538450199  0.627526061     1      0  0  0.693133972
#> 364  63  0.627526061  0.861556521     1      0  0  0.693133972
#> 365  63  0.861556521  1.102409116     1      0  0  0.693133972
#> 366  63  1.102409116  3.258602170     1      0  0  0.693133972
#> 367  63  3.258602170  6.293075161     1      0  0  0.693133972
#> 368  63  6.293075161 14.284947113     1      0  0  0.693133972
#> 369  63 14.284947113 17.246547226     1      0  0  0.693133972
#> 370  63 17.246547226 30.399024532     1      0  0  0.693133972
#> 371  63 30.399024532 33.538318472     0      1  0  0.693133972
#> 372  64  0.000000000  0.150317201     1      0  1 -0.139500325
#> 373  64  0.150317201  4.096807626     1      0  1 -0.139500325
#> 374  64  4.096807626 13.747458877     0      0  1 -0.139500325
#> 375  65  0.000000000 30.085791836     0      0  0 -3.310678727
#> 376  66  0.000000000  5.254560647     1      0  1  0.538465799
#> 377  66  5.254560647 19.785907300     0      0  1  0.538465799
#> 378  67  0.000000000  0.042599725     1      0  1  0.892485867
#> 379  67  0.042599725  0.460391154     1      0  1  0.892485867
#> 380  67  0.460391154  0.486884850     1      0  1  0.892485867
#> 381  67  0.486884850  0.623984366     1      0  1  0.892485867
#> 382  67  0.623984366  1.316361786     1      0  1  0.892485867
#> 383  67  1.316361786 16.813802408     0      1  1  0.892485867
#> 384  68  0.000000000  0.353305779     1      0  1  0.489462036
#> 385  68  0.353305779  1.326752035     1      0  1  0.489462036
#> 386  68  1.326752035  2.319360850     1      0  1  0.489462036
#> 387  68  2.319360850  2.344870833     0      0  1  0.489462036
#> 388  69  0.000000000  0.348996492     0      0  1 -1.196351747
#> 389  70  0.000000000  1.148963316     1      0  0  0.462737853
#> 390  70  1.148963316  1.312017315     1      0  0  0.462737853
#> 391  70  1.312017315  2.542578920     1      0  0  0.462737853
#> 392  70  2.542578920  5.151759989     1      0  0  0.462737853
#> 393  70  5.151759989 11.690276404     1      0  0  0.462737853
#> 394  70 11.690276404 60.000000000     0      0  0  0.462737853
#> 395  71  0.000000000  0.266150966     1      0  0  0.971703576
#> 396  71  0.266150966  0.349670849     0      1  0  0.971703576
#> 397  72  0.000000000 42.047029902     0      0  0 -1.472158964
#> 398  73  0.000000000  0.393912335     1      0  1  0.528964941
#> 399  73  0.393912335 50.322384926     1      0  1  0.528964941
#> 400  73 50.322384926 60.000000000     0      0  1  0.528964941
#> 401  74  0.000000000  0.226227290     0      1  0  2.454400353
#> 402  75  0.000000000  0.604137764     1      0  0 -1.649345480
#> 403  75  0.604137764  1.302897180     0      0  0 -1.649345480
#> 404  76  0.000000000  0.297104808     1      0  1  0.795805155
#> 405  76  0.297104808  1.442722956     1      0  1  0.795805155
#> 406  76  1.442722956  6.228937470     1      0  1  0.795805155
#> 407  76  6.228937470 33.654580313     1      0  1  0.795805155
#> 408  76 33.654580313 60.000000000     0      0  1  0.795805155
#> 409  77  0.000000000  0.247724744     1      0  0 -0.341293167
#> 410  77  0.247724744  0.883275948     1      0  0 -0.341293167
#> 411  77  0.883275948  0.965598205     1      0  0 -0.341293167
#> 412  77  0.965598205  1.267030058     1      0  0 -0.341293167
#> 413  77  1.267030058  2.136561426     1      0  0 -0.341293167
#> 414  77  2.136561426 11.737178714     1      0  0 -0.341293167
#> 415  77 11.737178714 19.006126729     1      0  0 -0.341293167
#> 416  77 19.006126729 19.508749921     1      0  0 -0.341293167
#> 417  77 19.508749921 33.068292801     1      0  0 -0.341293167
#> 418  77 33.068292801 37.221890340     0      0  0 -0.341293167
#> 419  78  0.000000000  1.634828342     1      0  0 -1.405253800
#> 420  78  1.634828342  2.166839239     0      0  0 -1.405253800
#> 421  79  0.000000000 18.849900991     0      1  1 -0.922960815
#> 422  80  0.000000000  0.057899323     1      0  0  0.009898130
#> 423  80  0.057899323  0.563149307     1      0  0  0.009898130
#> 424  80  0.563149307  1.729418601     1      0  0  0.009898130
#> 425  80  1.729418601  1.742868436     1      0  0  0.009898130
#> 426  80  1.742868436  2.184840182     1      0  0  0.009898130
#> 427  80  2.184840182  3.269702071     1      0  0  0.009898130
#> 428  80  3.269702071  6.823633670     0      0  0  0.009898130
#> 429  81  0.000000000  2.088983908     1      0  1 -0.408859774
#> 430  81  2.088983908 60.000000000     0      0  1 -0.408859774
#> 431  82  0.000000000 10.473374901     0      0  1 -1.388245289
#> 432  83  0.000000000  4.738025556     1      0  1 -0.264595238
#> 433  83  4.738025556 10.707105999     1      0  1 -0.264595238
#> 434  83 10.707105999 23.299277838     1      0  1 -0.264595238
#> 435  83 23.299277838 36.803331552     0      0  1 -0.264595238
#> 436  84  0.000000000  3.101080222     1      0  0 -0.947298279
#> 437  84  3.101080222  6.626583844     1      0  0 -0.947298279
#> 438  84  6.626583844 31.520187178     0      1  0 -0.947298279
#> 439  85  0.000000000  0.644340177     1      0  0  0.739521328
#> 440  85  0.644340177  0.710910608     1      0  0  0.739521328
#> 441  85  0.710910608  1.536251400     1      0  0  0.739521328
#> 442  85  1.536251400  1.816507927     1      0  0  0.739521328
#> 443  85  1.816507927  2.401143401     1      0  0  0.739521328
#> 444  85  2.401143401  2.613061991     1      0  0  0.739521328
#> 445  85  2.613061991  3.121227252     0      1  0  0.739521328
#> 446  86  0.000000000  0.016017404     1      0  0  0.896778709
#> 447  86  0.016017404  0.232698496     1      0  0  0.896778709
#> 448  86  0.232698496  0.577077685     1      0  0  0.896778709
#> 449  86  0.577077685  0.978526520     1      0  0  0.896778709
#> 450  86  0.978526520  1.057186346     1      0  0  0.896778709
#> 451  86  1.057186346  1.462097773     0      1  0  0.896778709
#> 452  87  0.000000000  0.895563396     1      0  0 -0.346000887
#> 453  87  0.895563396 33.465054977     0      0  0 -0.346000887
#> 454  88  0.000000000 22.899505699     0      0  1 -1.782057068
#> 455  89  0.000000000  0.037101618     1      0  0  0.464941753
#> 456  89  0.037101618  0.102710022     1      0  0  0.464941753
#> 457  89  0.102710022  0.216567111     1      0  0  0.464941753
#> 458  89  0.216567111  0.796068242     1      0  0  0.464941753
#> 459  89  0.796068242  0.958993995     1      0  0  0.464941753
#> 460  89  0.958993995  1.028313254     1      0  0  0.464941753
#> 461  89  1.028313254  1.074377107     0      0  0  0.464941753
#> 462  90  0.000000000 60.000000000     0      0  0 -1.951030610
#> 463  91  0.000000000  0.078056200     0      1  0 -0.516113340
#> 464  92  0.000000000  0.176685484     1      0  0  0.489080318
#> 465  92  0.176685484  0.296731331     1      0  0  0.489080318
#> 466  92  0.296731331  0.538848097     1      0  0  0.489080318
#> 467  92  0.538848097  0.571099060     1      0  0  0.489080318
#> 468  92  0.571099060  0.998071193     1      0  0  0.489080318
#> 469  92  0.998071193  1.283195611     1      0  0  0.489080318
#> 470  92  1.283195611  2.193886966     1      0  0  0.489080318
#> 471  92  2.193886966  3.611732953     1      0  0  0.489080318
#> 472  92  3.611732953  7.750845917     0      0  0  0.489080318
#> 473  93  0.000000000  0.025896790     1      0  1  0.902024726
#> 474  93  0.025896790  2.654534720     1      0  1  0.902024726
#> 475  93  2.654534720  2.711107298     1      0  1  0.902024726
#> 476  93  2.711107298  3.396050813     1      0  1  0.902024726
#> 477  93  3.396050813  4.747309685     0      0  1  0.902024726
#> 478  94  0.000000000  3.672871226     1      0  1  0.640362995
#> 479  94  3.672871226  5.452322593     1      0  1  0.640362995
#> 480  94  5.452322593 16.537795976     1      0  1  0.640362995
#> 481  94 16.537795976 21.891690916     1      0  1  0.640362995
#> 482  94 21.891690916 25.337334766     1      0  1  0.640362995
#> 483  94 25.337334766 60.000000000     0      0  1  0.640362995
#> 484  95  0.000000000  0.070926623     1      0  0  0.951208879
#> 485  95  0.070926623  0.423656815     1      0  0  0.951208879
#> 486  95  0.423656815  0.487280034     1      0  0  0.951208879
#> 487  95  0.487280034  0.496622564     1      0  0  0.951208879
#> 488  95  0.496622564  0.553466751     1      0  0  0.951208879
#> 489  95  0.553466751  0.605335217     1      0  0  0.951208879
#> 490  95  0.605335217  0.803361018     1      0  0  0.951208879
#> 491  95  0.803361018  0.965024233     0      1  0  0.951208879
#> 492  96  0.000000000  3.769555449     0      1  1 -0.599123210
#> 493  97  0.000000000  1.274006209     0      1  0 -1.330694993
#> 494  98  0.000000000 11.432728756     1      0  0 -0.592209746
#> 495  98 11.432728756 11.998121025     1      0  0 -0.592209746
#> 496  98 11.998121025 14.377420871     1      0  0 -0.592209746
#> 497  98 14.377420871 22.412248553     1      0  0 -0.592209746
#> 498  98 22.412248553 23.615610800     1      0  0 -0.592209746
#> 499  98 23.615610800 45.509140172     1      0  0 -0.592209746
#> 500  98 45.509140172 59.117118140     0      1  0 -0.592209746
#> 501  99  0.000000000  0.024035847     1      0  0  1.801050856
#> 502  99  0.024035847  0.169182346     1      0  0  1.801050856
#> 503  99  0.169182346  0.204678212     1      0  0  1.801050856
#> 504  99  0.204678212  0.429791121     1      0  0  1.801050856
#> 505  99  0.429791121  0.564102773     1      0  0  1.801050856
#> 506  99  0.564102773  0.612301930     1      0  0  1.801050856
#> 507  99  0.612301930  0.920473254     1      0  0  1.801050856
#> 508  99  0.920473254  1.029332820     1      0  0  1.801050856
#> 509  99  1.029332820  1.351443755     1      0  0  1.801050856
#> 510  99  1.351443755  1.689399361     0      1  0  1.801050856
#> 511 100  0.000000000  0.062282158     1      0  1  1.055338591
#> 512 100  0.062282158  0.092470102     1      0  1  1.055338591
#> 513 100  0.092470102  0.099136473     1      0  1  1.055338591
#> 514 100  0.099136473  0.119418775     1      0  1  1.055338591
#> 515 100  0.119418775  0.494375485     1      0  1  1.055338591
#> 516 100  0.494375485  0.535604140     1      0  1  1.055338591
#> 517 100  0.535604140  0.928665456     1      0  1  1.055338591
#> 518 100  0.928665456  2.430407324     1      0  1  1.055338591
#> 519 100  2.430407324  2.924293729     1      0  1  1.055338591
#> 520 100  2.924293729  5.242506460     1      0  1  1.055338591
#> 521 100  5.242506460  5.727066391     1      0  1  1.055338591
#> 522 100  5.727066391  7.211164372     1      0  1  1.055338591
#> 523 100  7.211164372  8.749865224     1      0  1  1.055338591
#> 524 100  8.749865224  9.247636836     1      0  1  1.055338591
#> 525 100  9.247636836 10.889850475     1      0  1  1.055338591
#> 526 100 10.889850475 11.144609855     1      0  1  1.055338591
#> 527 100 11.144609855 11.155463685     1      0  1  1.055338591
#> 528 100 11.155463685 42.939965866     1      0  1  1.055338591
#> 529 100 42.939965866 44.020624512     0      0  1  1.055338591