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

simGSC(
n,
summary = FALSE,
para,
xmat,
censoring,
frailty,
tau,
origin,
Lam0,
Haz0
)

## Arguments

n number of observation. a logical value indicating whether a brief data summary will be printed. a list of numerical vectors for the regression coefficients in the joint scale-change model. The names of the list elements are alpha, beta, eta, and theta, correspond to $$\alpha$$, $$\beta$$, $$\eta$$, and $$\theta$$ in the joint scale-change model, respectively. See Details for reReg. an optional matrix specifying the design matrix. a numeric variable specifying the censoring times for each of the $$n$$ observation. a numeric variable specifying the frailty variable. a numeric value specifying the maximum observation time. a numeric value specifying the time origin. is an optional function that specifies the baseline cumulative rate function. When left-unspecified, the recurrent events are generated using the baseline rate function of $$\lambda_0(t) = \frac{2}{1 + t},$$ or equivalently, the cumulative rate function of $$\Lambda_0(t) = 2\log(1 + t).$$ is an optional function that specifies the baseline hazard function. When left-unspecified, the recurrent events are generated using the baseline hazard function $$h_0(t) = \frac{1}{5(1 + t)},$$ or equivalently, the cumulative hazard function of $$H_0(t) = \log(1 + t) / 5.$$

## Details

The function simGSC() 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.

Under the default settings, the simGSC() function assumes $$p = 2$$ and the regression parameters to be $$\alpha = \eta = (0, 0)^\top$$, and $$\beta = \theta = (1, 1)^\top$$. When the xmat argument is not specified, the simGSC() function assumes $$X_i$$ is a two-dimensional vector $$X_i = (X_{i1}, X_{i2}), i = 1, \ldots, n$$, where $$X_{i1}$$ is a Bernoulli variable with rate 0.5 and $$X_{i2}$$ is a standard normal variable. With the default xmat, the censoring time $C$ is generated from an independent uniform distribution in $$[0, 2\tau X_{i1} + 2Z^2\tau(1 - X_{i1})]$$. Thus, the censoring distribution is covariate dependent and is informative when $$Z$$ is not a constant. When the frailty argument is not specified, the frailty variable $$Z$$ is generated from a gamma distribution with a unit mean and a variance of 0.25. The default values for tau and origin are 60 and 0, respectively. When arguments Lam0 and Haz0 are left unspecified, the simGSC() function uses $$\Lambda_0(t) = 2\log(1 + t)$$ and $$H_0(t) = \log(1 + t) / 5$$, respectively. This is equivalent to setting Lam0 = function(x) 2 * log(1 + x) and Haz0 = function(x) log(1 + x) / 5. Overall, the default specifications generate the recurrent events and the terminal events from the model: $$\lambda(t) = \displaystyle \frac{2Z}{1 + te^{-X_{i1} - X_{i2}}}, h(t) = \displaystyle \frac{Z}{5(1 + te^{X_{i1} + X_{i2}})}, t\in[0, 60].$$ See online vignette for more examples.

reReg

## Examples

set.seed(123)
simGSC(100, summary = TRUE)
#> Call:
#> simGSC(n = 100, summary = TRUE)
#>
#> Summary:
#> Sample size:                                    100
#> Number of recurrent event observed:             369
#> Average number of recurrent event per subject:  3.69
#> Proportion of subjects with a terminal event:   0.52
#> Median time-to-terminal event:                  13.874
#>
#> #>      id      t.start       t.stop event status x1           x2
#> 1     1 0.000000e+00 7.673334e-01     0      1  1  0.157076450
#> 2     2 0.000000e+00 4.792243e-01     1      0  0  0.922419336
#> 3     2 4.792243e-01 5.278326e-01     1      0  0  0.922419336
#> 4     2 5.278326e-01 5.352025e-01     1      0  0  0.922419336
#> 5     2 5.352025e-01 5.390913e-01     0      1  0  0.922419336
#> 6     3 0.000000e+00 5.938063e+00     1      0  1 -0.490958575
#> 7     3 5.938063e+00 2.459264e+01     0      0  1 -0.490958575
#> 8     4 0.000000e+00 6.064374e-01     1      0  1  1.098001882
#> 9     4 6.064374e-01 3.449541e+00     0      1  1  1.098001882
#> 10    5 0.000000e+00 1.039255e-02     1      0  0 -0.102333833
#> 11    5 1.039255e-02 8.348449e-01     1      0  0 -0.102333833
#> 12    5 8.348449e-01 1.241384e+00     1      0  0 -0.102333833
#> 13    5 1.241384e+00 2.128515e+00     1      0  0 -0.102333833
#> 14    5 2.128515e+00 2.263810e+00     1      0  0 -0.102333833
#> 15    5 2.263810e+00 2.787350e+00     1      0  0 -0.102333833
#> 16    5 2.787350e+00 5.155177e+00     1      0  0 -0.102333833
#> 17    5 5.155177e+00 6.851851e+00     1      0  0 -0.102333833
#> 18    5 6.851851e+00 7.713927e+00     1      0  0 -0.102333833
#> 19    5 7.713927e+00 9.232733e+00     1      0  0 -0.102333833
#> 20    5 9.232733e+00 1.022518e+01     1      0  0 -0.102333833
#> 21    5 1.022518e+01 1.034746e+01     1      0  0 -0.102333833
#> 22    5 1.034746e+01 1.635524e+01     1      0  0 -0.102333833
#> 23    5 1.635524e+01 1.967031e+01     1      0  0 -0.102333833
#> 24    5 1.967031e+01 2.106709e+01     1      0  0 -0.102333833
#> 25    5 2.106709e+01 2.149465e+01     1      0  0 -0.102333833
#> 26    5 2.149465e+01 3.142128e+01     1      0  0 -0.102333833
#> 27    5 3.142128e+01 3.863199e+01     1      0  0 -0.102333833
#> 28    5 3.863199e+01 4.026081e+01     1      0  0 -0.102333833
#> 29    5 4.026081e+01 6.000000e+01     0      0  0 -0.102333833
#> 30    6 0.000000e+00 9.999753e-01     1      0  0  0.487571468
#> 31    6 9.999753e-01 2.435904e+00     1      0  0  0.487571468
#> 32    6 2.435904e+00 6.000000e+01     0      0  0  0.487571468
#> 33    7 0.000000e+00 8.164655e-02     1      0  0 -0.433783058
#> 34    7 8.164655e-02 1.979892e+00     1      0  0 -0.433783058
#> 35    7 1.979892e+00 1.035070e+01     0      0  0 -0.433783058
#> 36    8 0.000000e+00 6.321277e-01     1      0  0 -0.250593796
#> 37    8 6.321277e-01 2.299605e+00     1      0  0 -0.250593796
#> 38    8 2.299605e+00 5.138238e+00     0      0  0 -0.250593796
#> 39    9 0.000000e+00 1.779847e-01     0      1  0  0.392795581
#> 40   10 0.000000e+00 4.900986e+00     1      0  1 -1.051123662
#> 41   10 4.900986e+00 7.380450e+00     0      1  1 -1.051123662
#> 42   11 0.000000e+00 1.237283e+00     1      0  0 -0.021102465
#> 43   11 1.237283e+00 2.230570e+00     0      0  0 -0.021102465
#> 44   12 0.000000e+00 9.890380e-04     1      0  1 -0.202404707
#> 45   12 9.890380e-04 3.381851e+00     0      1  1 -0.202404707
#> 46   13 0.000000e+00 4.833602e-01     1      0  1 -0.056382983
#> 47   13 4.833602e-01 9.760000e+00     1      0  1 -0.056382983
#> 48   13 9.760000e+00 1.104869e+01     1      0  1 -0.056382983
#> 49   13 1.104869e+01 3.886510e+01     1      0  1 -0.056382983
#> 50   13 3.886510e+01 6.000000e+01     0      0  1 -0.056382983
#> 51   14 0.000000e+00 2.023218e-01     0      1  1  0.898570220
#> 52   15 0.000000e+00 7.668470e-01     1      0  0 -0.405163129
#> 53   15 7.668470e-01 8.195277e-01     1      0  0 -0.405163129
#> 54   15 8.195277e-01 1.186631e+00     1      0  0 -0.405163129
#> 55   15 1.186631e+00 2.662091e+00     1      0  0 -0.405163129
#> 56   15 2.662091e+00 2.687997e+00     1      0  0 -0.405163129
#> 57   15 2.687997e+00 4.726670e+00     1      0  0 -0.405163129
#> 58   15 4.726670e+00 4.933471e+00     1      0  0 -0.405163129
#> 59   15 4.933471e+00 7.796493e+00     1      0  0 -0.405163129
#> 60   15 7.796493e+00 1.208258e+01     1      0  0 -0.405163129
#> 61   15 1.208258e+01 1.744109e+01     1      0  0 -0.405163129
#> 62   15 1.744109e+01 1.925079e+01     1      0  0 -0.405163129
#> 63   15 1.925079e+01 2.090413e+01     1      0  0 -0.405163129
#> 64   15 2.090413e+01 2.369241e+01     1      0  0 -0.405163129
#> 65   15 2.369241e+01 2.789842e+01     1      0  0 -0.405163129
#> 66   15 2.789842e+01 4.045521e+01     1      0  0 -0.405163129
#> 67   15 4.045521e+01 4.101196e+01     0      0  0 -0.405163129
#> 68   16 0.000000e+00 1.347988e+00     0      1  1  0.950450037
#> 69   17 0.000000e+00 9.322742e-01     1      0  0  0.354477220
#> 70   17 9.322742e-01 3.145312e+00     0      1  0  0.354477220
#> 71   18 0.000000e+00 1.848603e+00     0      1  1  0.368097387
#> 72   19 0.000000e+00 2.070892e+01     0      0  0  0.682888277
#> 73   20 0.000000e+00 1.837757e-01     1      0  0 -0.288131946
#> 74   20 1.837757e-01 1.567255e+00     1      0  0 -0.288131946
#> 75   20 1.567255e+00 3.649105e+00     1      0  0 -0.288131946
#> 76   20 3.649105e+00 1.488528e+01     1      0  0 -0.288131946
#> 77   20 1.488528e+01 2.190166e+01     1      0  0 -0.288131946
#> 78   20 2.190166e+01 3.717587e+01     1      0  0 -0.288131946
#> 79   20 3.717587e+01 4.582297e+01     0      0  0 -0.288131946
#> 80   21 0.000000e+00 7.398890e+00     0      0  0 -0.402366160
#> 81   22 0.000000e+00 3.573538e-01     1      0  0 -0.267532906
#> 82   22 3.573538e-01 8.493560e-01     1      0  0 -0.267532906
#> 83   22 8.493560e-01 1.142279e+01     0      0  0 -0.267532906
#> 84   23 0.000000e+00 6.460289e+00     1      0  0  0.395773955
#> 85   23 6.460289e+00 7.835392e+00     1      0  0  0.395773955
#> 86   23 7.835392e+00 1.951356e+01     0      0  0  0.395773955
#> 87   24 0.000000e+00 9.008201e-02     1      0  0 -0.353803575
#> 88   24 9.008201e-02 1.565315e-01     1      0  0 -0.353803575
#> 89   24 1.565315e-01 3.860905e-01     1      0  0 -0.353803575
#> 90   24 3.860905e-01 1.173988e+00     1      0  0 -0.353803575
#> 91   24 1.173988e+00 1.405757e+00     1      0  0 -0.353803575
#> 92   24 1.405757e+00 1.467210e+00     1      0  0 -0.353803575
#> 93   24 1.467210e+00 9.443959e+00     1      0  0 -0.353803575
#> 94   24 9.443959e+00 3.774314e+01     0      0  0 -0.353803575
#> 95   25 0.000000e+00 2.057282e+00     1      0  1 -0.637771686
#> 96   25 2.057282e+00 2.514794e+00     1      0  1 -0.637771686
#> 97   25 2.514794e+00 4.213940e+00     1      0  1 -0.637771686
#> 98   25 4.213940e+00 6.067740e+00     1      0  1 -0.637771686
#> 99   25 6.067740e+00 1.180050e+01     0      1  1 -0.637771686
#> 100  26 0.000000e+00 1.348991e+00     1      0  0  1.187732231
#> 101  26 1.348991e+00 6.000000e+01     0      0  0  1.187732231
#> 102  27 0.000000e+00 1.565897e-02     0      1  1 -0.546794874
#> 103  28 0.000000e+00 2.253134e-01     1      0  0  0.096220791
#> 104  28 2.253134e-01 4.033071e-01     1      0  0  0.096220791
#> 105  28 4.033071e-01 4.364948e-01     1      0  0  0.096220791
#> 106  28 4.364948e-01 4.555481e-01     1      0  0  0.096220791
#> 107  28 4.555481e-01 6.614891e-01     1      0  0  0.096220791
#> 108  28 6.614891e-01 1.467013e+00     1      0  0  0.096220791
#> 109  28 1.467013e+00 4.160644e+00     1      0  0  0.096220791
#> 110  28 4.160644e+00 1.436581e+01     1      0  0  0.096220791
#> 111  28 1.436581e+01 2.927817e+01     1      0  0  0.096220791
#> 112  28 2.927817e+01 3.924106e+01     0      1  0  0.096220791
#> 113  29 0.000000e+00 2.255300e-02     1      0  0 -0.063080191
#> 114  29 2.255300e-02 2.632242e-02     1      0  0 -0.063080191
#> 115  29 2.632242e-02 2.011347e-01     1      0  0 -0.063080191
#> 116  29 2.011347e-01 2.380527e-01     1      0  0 -0.063080191
#> 117  29 2.380527e-01 2.910620e-01     1      0  0 -0.063080191
#> 118  29 2.910620e-01 5.764885e-01     1      0  0 -0.063080191
#> 119  29 5.764885e-01 7.146380e-01     1      0  0 -0.063080191
#> 120  29 7.146380e-01 1.308733e+00     1      0  0 -0.063080191
#> 121  29 1.308733e+00 2.930865e+00     0      0  0 -0.063080191
#> 122  30 0.000000e+00 2.783760e-02     1      0  0 -0.694216070
#> 123  30 2.783760e-02 2.352572e-01     1      0  0 -0.694216070
#> 124  30 2.352572e-01 4.394143e-01     1      0  0 -0.694216070
#> 125  30 4.394143e-01 3.353034e+00     1      0  0 -0.694216070
#> 126  30 3.353034e+00 5.233463e+00     1      0  0 -0.694216070
#> 127  30 5.233463e+00 1.600442e+01     1      0  0 -0.694216070
#> 128  30 1.600442e+01 1.927304e+01     1      0  0 -0.694216070
#> 129  30 1.927304e+01 2.165265e+01     1      0  0 -0.694216070
#> 130  30 2.165265e+01 2.279783e+01     1      0  0 -0.694216070
#> 131  30 2.279783e+01 2.528339e+01     1      0  0 -0.694216070
#> 132  30 2.528339e+01 2.545949e+01     1      0  0 -0.694216070
#> 133  30 2.545949e+01 2.989786e+01     1      0  0 -0.694216070
#> 134  30 2.989786e+01 3.035262e+01     1      0  0 -0.694216070
#> 135  30 3.035262e+01 4.870705e+01     0      0  0 -0.694216070
#> 136  31 0.000000e+00 1.151866e+00     1      0  0  0.234951096
#> 137  31 1.151866e+00 2.943520e+00     1      0  0  0.234951096
#> 138  31 2.943520e+00 3.202859e+00     0      1  0  0.234951096
#> 139  32 0.000000e+00 6.000000e+01     0      0  1  0.480191179
#> 140  33 0.000000e+00 2.068138e+00     0      1  1 -0.002570644
#> 141  34 0.000000e+00 8.226492e-01     1      0  0 -0.435232221
#> 142  34 8.226492e-01 1.295081e+00     1      0  0 -0.435232221
#> 143  34 1.295081e+00 1.430225e+00     1      0  0 -0.435232221
#> 144  34 1.430225e+00 1.627231e+00     1      0  0 -0.435232221
#> 145  34 1.627231e+00 1.746745e+00     1      0  0 -0.435232221
#> 146  34 1.746745e+00 1.765047e+00     1      0  0 -0.435232221
#> 147  34 1.765047e+00 1.875574e+00     0      1  0 -0.435232221
#> 148  35 0.000000e+00 5.456630e-01     1      0  0 -0.231439520
#> 149  35 5.456630e-01 1.172969e+00     1      0  0 -0.231439520
#> 150  35 1.172969e+00 1.860006e+00     1      0  0 -0.231439520
#> 151  35 1.860006e+00 3.061952e+00     1      0  0 -0.231439520
#> 152  35 3.061952e+00 4.141062e+00     1      0  0 -0.231439520
#> 153  35 4.141062e+00 4.304177e+00     1      0  0 -0.231439520
#> 154  35 4.304177e+00 7.098237e+00     1      0  0 -0.231439520
#> 155  35 7.098237e+00 7.162430e+00     1      0  0 -0.231439520
#> 156  35 7.162430e+00 7.252725e+00     1      0  0 -0.231439520
#> 157  35 7.252725e+00 1.065667e+01     1      0  0 -0.231439520
#> 158  35 1.065667e+01 1.412273e+01     1      0  0 -0.231439520
#> 159  35 1.412273e+01 1.512011e+01     1      0  0 -0.231439520
#> 160  35 1.512011e+01 2.281397e+01     1      0  0 -0.231439520
#> 161  35 2.281397e+01 2.527802e+01     1      0  0 -0.231439520
#> 162  35 2.527802e+01 4.807647e+01     1      0  0 -0.231439520
#> 163  35 4.807647e+01 5.579706e+01     1      0  0 -0.231439520
#> 164  35 5.579706e+01 6.000000e+01     0      0  0 -0.231439520
#> 165  36 0.000000e+00 4.132026e-01     1      0  0 -0.955575628
#> 166  36 4.132026e-01 1.045911e+00     1      0  0 -0.955575628
#> 167  36 1.045911e+00 1.326520e+00     1      0  0 -0.955575628
#> 168  36 1.326520e+00 1.331590e+00     1      0  0 -0.955575628
#> 169  36 1.331590e+00 3.310202e+00     1      0  0 -0.955575628
#> 170  36 3.310202e+00 6.340162e+00     1      0  0 -0.955575628
#> 171  36 6.340162e+00 7.227096e+00     1      0  0 -0.955575628
#> 172  36 7.227096e+00 7.587522e+00     1      0  0 -0.955575628
#> 173  36 7.587522e+00 1.670387e+01     1      0  0 -0.955575628
#> 174  36 1.670387e+01 1.926063e+01     0      0  0 -0.955575628
#> 175  37 0.000000e+00 2.457078e-01     1      0  1  0.184908022
#> 176  37 2.457078e-01 1.923592e+00     0      1  1  0.184908022
#> 177  38 0.000000e+00 8.140886e-01     0      1  1 -0.231144029
#> 178  39 0.000000e+00 7.025056e-01     0      1  1  0.160977946
#> 179  40 0.000000e+00 3.212027e+00     1      0  0 -0.142000695
#> 180  40 3.212027e+00 1.111957e+01     1      0  0 -0.142000695
#> 181  40 1.111957e+01 1.395034e+01     1      0  0 -0.142000695
#> 182  40 1.395034e+01 2.014947e+01     1      0  0 -0.142000695
#> 183  40 2.014947e+01 3.307767e+01     0      1  0 -0.142000695
#> 184  41 0.000000e+00 1.181103e+01     1      0  1  0.545928222
#> 185  41 1.181103e+01 1.320714e+01     0      1  1  0.545928222
#> 186  42 0.000000e+00 6.611685e-02     0      1  0  0.080108181
#> 187  43 0.000000e+00 6.652349e-01     1      0  0  1.354084142
#> 188  43 6.652349e-01 1.497815e+00     0      0  0  1.354084142
#> 189  44 0.000000e+00 2.076827e+00     1      0  0  0.143144965
#> 190  44 2.076827e+00 3.273389e+00     1      0  0  0.143144965
#> 191  44 3.273389e+00 1.050416e+01     0      0  0  0.143144965
#> 192  45 0.000000e+00 1.906165e+00     1      0  0 -0.016255125
#> 193  45 1.906165e+00 2.478052e+00     1      0  0 -0.016255125
#> 194  45 2.478052e+00 2.871168e+00     0      0  0 -0.016255125
#> 195  46 0.000000e+00 5.602840e-01     1      0  0 -0.494839010
#> 196  46 5.602840e-01 6.831704e-01     1      0  0 -0.494839010
#> 197  46 6.831704e-01 7.342415e-01     1      0  0 -0.494839010
#> 198  46 7.342415e-01 1.836757e+00     1      0  0 -0.494839010
#> 199  46 1.836757e+00 1.943934e+00     1      0  0 -0.494839010
#> 200  46 1.943934e+00 3.023834e+00     1      0  0 -0.494839010
#> 201  46 3.023834e+00 3.613537e+00     1      0  0 -0.494839010
#> 202  46 3.613537e+00 5.032584e+00     1      0  0 -0.494839010
#> 203  46 5.032584e+00 1.016109e+01     0      0  0 -0.494839010
#> 204  47 0.000000e+00 6.108031e+00     0      1  1  0.105904964
#> 205  48 0.000000e+00 1.300019e+00     1      0  1 -0.486008767
#> 206  48 1.300019e+00 2.704357e+00     1      0  1 -0.486008767
#> 207  48 2.704357e+00 8.397697e+00     0      1  1 -0.486008767
#> 208  49 0.000000e+00 2.276894e-01     0      1  1  0.274612007
#> 209  50 0.000000e+00 1.117742e+00     1      0  0 -0.524510765
#> 210  50 1.117742e+00 4.520894e+00     1      0  0 -0.524510765
#> 211  50 4.520894e+00 1.407878e+01     0      0  0 -0.524510765
#> 212  51 0.000000e+00 6.431133e-02     1      0  0  0.224566967
#> 213  51 6.431133e-02 1.621943e+00     1      0  0  0.224566967
#> 214  51 1.621943e+00 2.327757e+00     1      0  0  0.224566967
#> 215  51 2.327757e+00 3.365998e+00     1      0  0  0.224566967
#> 216  51 3.365998e+00 4.012916e+00     0      0  0  0.224566967
#> 217  52 0.000000e+00 3.871640e+00     0      1  1 -0.192927826
#> 218  53 0.000000e+00 2.365260e+00     1      0  1 -0.785067761
#> 219  53 2.365260e+00 5.571977e+00     1      0  1 -0.785067761
#> 220  53 5.571977e+00 1.562437e+01     1      0  1 -0.785067761
#> 221  53 1.562437e+01 2.276292e+01     1      0  1 -0.785067761
#> 222  53 2.276292e+01 3.968548e+01     1      0  1 -0.785067761
#> 223  53 3.968548e+01 6.000000e+01     0      0  1 -0.785067761
#> 224  54 0.000000e+00 3.363785e+00     1      0  0  0.613471301
#> 225  54 3.363785e+00 3.434397e+00     0      1  0  0.613471301
#> 226  55 0.000000e+00 9.101713e-02     0      1  1  0.333347198
#> 227  56 0.000000e+00 1.247283e+00     1      0  0 -0.575801582
#> 228  56 1.247283e+00 1.304254e+00     1      0  0 -0.575801582
#> 229  56 1.304254e+00 1.506118e+00     1      0  0 -0.575801582
#> 230  56 1.506118e+00 2.045403e+00     1      0  0 -0.575801582
#> 231  56 2.045403e+00 6.889056e+00     1      0  0 -0.575801582
#> 232  56 6.889056e+00 9.105803e+00     0      0  0 -0.575801582
#> 233  57 0.000000e+00 3.202656e+00     1      0  0 -0.080394242
#> 234  57 3.202656e+00 3.764321e+00     1      0  0 -0.080394242
#> 235  57 3.764321e+00 2.446862e+01     0      0  0 -0.080394242
#> 236  58 0.000000e+00 8.882910e-01     1      0  1 -0.486456888
#> 237  58 8.882910e-01 6.484381e+00     1      0  1 -0.486456888
#> 238  58 6.484381e+00 1.755385e+01     0      0  1 -0.486456888
#> 239  59 0.000000e+00 1.139834e+00     1      0  0 -0.305230830
#> 240  59 1.139834e+00 1.608917e+00     1      0  0 -0.305230830
#> 241  59 1.608917e+00 1.958803e+00     1      0  0 -0.305230830
#> 242  59 1.958803e+00 2.085734e+00     1      0  0 -0.305230830
#> 243  59 2.085734e+00 2.539565e+00     1      0  0 -0.305230830
#> 244  59 2.539565e+00 3.139280e+00     1      0  0 -0.305230830
#> 245  59 3.139280e+00 5.039785e+00     1      0  0 -0.305230830
#> 246  59 5.039785e+00 6.848964e+00     1      0  0 -0.305230830
#> 247  59 6.848964e+00 7.004673e+00     1      0  0 -0.305230830
#> 248  59 7.004673e+00 9.042904e+00     1      0  0 -0.305230830
#> 249  59 9.042904e+00 1.133672e+01     1      0  0 -0.305230830
#> 250  59 1.133672e+01 1.754341e+01     1      0  0 -0.305230830
#> 251  59 1.754341e+01 3.615164e+01     1      0  0 -0.305230830
#> 252  59 3.615164e+01 3.792654e+01     1      0  0 -0.305230830
#> 253  59 3.792654e+01 4.108082e+01     1      0  0 -0.305230830
#> 254  59 4.108082e+01 4.456794e+01     1      0  0 -0.305230830
#> 255  59 4.456794e+01 6.000000e+01     0      0  0 -0.305230830
#> 256  60 0.000000e+00 3.574408e-01     1      0  0  0.249638438
#> 257  60 3.574408e-01 6.410603e-01     1      0  0  0.249638438
#> 258  60 6.410603e-01 6.881801e+00     1      0  0  0.249638438
#> 259  60 6.881801e+00 7.772954e+00     1      0  0  0.249638438
#> 260  60 7.772954e+00 2.016170e+01     1      0  0  0.249638438
#> 261  60 2.016170e+01 3.020942e+01     0      0  0  0.249638438
#> 262  61 0.000000e+00 7.083687e+00     0      0  0  0.439682070
#> 263  62 0.000000e+00 1.246346e+00     0      1  1  0.461564620
#> 264  63 0.000000e+00 2.515486e-01     1      0  0  0.346566986
#> 265  63 2.515486e-01 4.125132e-01     1      0  0  0.346566986
#> 266  63 4.125132e-01 1.013612e+00     1      0  0  0.346566986
#> 267  63 1.013612e+00 4.656791e+00     1      0  0  0.346566986
#> 268  63 4.656791e+00 8.933061e+00     0      0  0  0.346566986
#> 269  64 0.000000e+00 6.485166e-01     0      1  1 -0.069750162
#> 270  65 0.000000e+00 4.932926e-02     1      0  0 -1.655339363
#> 271  65 4.932926e-02 6.261737e-02     1      0  0 -1.655339363
#> 272  65 6.261737e-02 2.559807e-01     1      0  0 -1.655339363
#> 273  65 2.559807e-01 3.573117e-01     1      0  0 -1.655339363
#> 274  65 3.573117e-01 4.295981e-01     1      0  0 -1.655339363
#> 275  65 4.295981e-01 4.663109e-01     1      0  0 -1.655339363
#> 276  65 4.663109e-01 1.022415e+00     1      0  0 -1.655339363
#> 277  65 1.022415e+00 2.527235e+00     1      0  0 -1.655339363
#> 278  65 2.527235e+00 3.583408e+00     1      0  0 -1.655339363
#> 279  65 3.583408e+00 3.630561e+00     1      0  0 -1.655339363
#> 280  65 3.630561e+00 4.466413e+00     1      0  0 -1.655339363
#> 281  65 4.466413e+00 4.721404e+00     1      0  0 -1.655339363
#> 282  65 4.721404e+00 5.067057e+00     1      0  0 -1.655339363
#> 283  65 5.067057e+00 5.700125e+00     1      0  0 -1.655339363
#> 284  65 5.700125e+00 6.234603e+00     1      0  0 -1.655339363
#> 285  65 6.234603e+00 6.317163e+00     1      0  0 -1.655339363
#> 286  65 6.317163e+00 7.784869e+00     1      0  0 -1.655339363
#> 287  65 7.784869e+00 7.849777e+00     1      0  0 -1.655339363
#> 288  65 7.849777e+00 9.430274e+00     1      0  0 -1.655339363
#> 289  65 9.430274e+00 1.031342e+01     1      0  0 -1.655339363
#> 290  65 1.031342e+01 1.374463e+01     1      0  0 -1.655339363
#> 291  65 1.374463e+01 1.422748e+01     1      0  0 -1.655339363
#> 292  65 1.422748e+01 2.087489e+01     1      0  0 -1.655339363
#> 293  65 2.087489e+01 3.203278e+01     1      0  0 -1.655339363
#> 294  65 3.203278e+01 3.603228e+01     1      0  0 -1.655339363
#> 295  65 3.603228e+01 6.000000e+01     0      0  0 -1.655339363
#> 296  66 0.000000e+00 6.716704e+00     0      1  1  0.269232900
#> 297  67 0.000000e+00 2.231122e-01     0      1  1  0.446242933
#> 298  68 0.000000e+00 1.516876e+00     0      1  1  0.244731018
#> 299  69 0.000000e+00 1.867339e-01     1      0  1 -0.598175873
#> 300  69 1.867339e-01 1.179108e+00     1      0  1 -0.598175873
#> 301  69 1.179108e+00 1.400892e+00     1      0  1 -0.598175873
#> 302  69 1.400892e+00 1.923110e+01     0      1  1 -0.598175873
#> 303  70 0.000000e+00 4.806616e-01     1      0  0  0.231368927
#> 304  70 4.806616e-01 1.604211e+00     1      0  0  0.231368927
#> 305  70 1.604211e+00 1.652917e+00     1      0  0  0.231368927
#> 306  70 1.652917e+00 1.982361e+00     1      0  0  0.231368927
#> 307  70 1.982361e+00 6.000000e+01     0      0  0  0.231368927
#> 308  71 0.000000e+00 4.890369e-02     1      0  0  0.485851788
#> 309  71 4.890369e-02 2.111682e-01     1      0  0  0.485851788
#> 310  71 2.111682e-01 5.027649e+00     0      0  0  0.485851788
#> 311  72 0.000000e+00 1.584647e-01     1      0  0 -0.736079482
#> 312  72 1.584647e-01 1.504156e+00     1      0  0 -0.736079482
#> 313  72 1.504156e+00 1.735140e+00     1      0  0 -0.736079482
#> 314  72 1.735140e+00 1.796161e+00     1      0  0 -0.736079482
#> 315  72 1.796161e+00 1.148065e+01     1      0  0 -0.736079482
#> 316  72 1.148065e+01 1.369229e+01     1      0  0 -0.736079482
#> 317  72 1.369229e+01 2.076923e+01     1      0  0 -0.736079482
#> 318  72 2.076923e+01 2.164684e+01     1      0  0 -0.736079482
#> 319  72 2.164684e+01 2.590099e+01     1      0  0 -0.736079482
#> 320  72 2.590099e+01 2.841050e+01     1      0  0 -0.736079482
#> 321  72 2.841050e+01 4.029755e+01     1      0  0 -0.736079482
#> 322  72 4.029755e+01 4.740414e+01     0      0  0 -0.736079482
#> 323  73 0.000000e+00 1.121501e+00     1      0  1  0.264482470
#> 324  73 1.121501e+00 1.653021e+00     1      0  1  0.264482470
#> 325  73 1.653021e+00 1.002727e+01     1      0  1  0.264482470
#> 326  73 1.002727e+01 1.639212e+01     0      1  1  0.264482470
#> 327  74 0.000000e+00 2.691809e-01     0      1  0  1.227200176
#> 328  75 0.000000e+00 9.133437e-02     1      0  0 -0.824672740
#> 329  75 9.133437e-02 9.929944e-02     1      0  0 -0.824672740
#> 330  75 9.929944e-02 2.405427e-01     0      1  0 -0.824672740
#> 331  76 0.000000e+00 4.722508e-01     0      1  1  0.397902578
#> 332  77 0.000000e+00 1.786242e-01     1      0  0 -0.170646583
#> 333  77 1.786242e-01 2.187578e-01     1      0  0 -0.170646583
#> 334  77 2.187578e-01 2.331823e+00     1      0  0 -0.170646583
#> 335  77 2.331823e+00 3.317999e+00     1      0  0 -0.170646583
#> 336  77 3.317999e+00 3.434961e+00     1      0  0 -0.170646583
#> 337  77 3.434961e+00 3.916352e+00     0      1  0 -0.170646583
#> 338  78 0.000000e+00 1.263900e-01     1      0  0 -0.702626900
#> 339  78 1.263900e-01 1.666562e+00     1      0  0 -0.702626900
#> 340  78 1.666562e+00 4.108156e+00     1      0  0 -0.702626900
#> 341  78 4.108156e+00 6.417344e+00     1      0  0 -0.702626900
#> 342  78 6.417344e+00 8.272144e+00     1      0  0 -0.702626900
#> 343  78 8.272144e+00 1.384900e+01     1      0  0 -0.702626900
#> 344  78 1.384900e+01 1.677600e+01     1      0  0 -0.702626900
#> 345  78 1.677600e+01 1.938759e+01     0      0  0 -0.702626900
#> 346  79 0.000000e+00 3.379712e-01     0      1  1 -0.461480408
#> 347  80 0.000000e+00 3.171416e-01     1      0  0  0.004949065
#> 348  80 3.171416e-01 4.060231e-01     1      0  0  0.004949065
#> 349  80 4.060231e-01 9.453294e-01     1      0  0  0.004949065
#> 350  80 9.453294e-01 1.340897e+00     1      0  0  0.004949065
#> 351  80 1.340897e+00 1.356481e+00     1      0  0  0.004949065
#> 352  80 1.356481e+00 2.047346e+00     1      0  0  0.004949065
#> 353  80 2.047346e+00 2.181133e+00     1      0  0  0.004949065
#> 354  80 2.181133e+00 2.384316e+00     1      0  0  0.004949065
#> 355  80 2.384316e+00 3.191958e+00     1      0  0  0.004949065
#> 356  80 3.191958e+00 3.777452e+00     1      0  0  0.004949065
#> 357  80 3.777452e+00 3.949139e+00     0      1  0  0.004949065
#> 358  81 0.000000e+00 1.921153e-01     0      1  1 -0.204429887
#> 359  82 0.000000e+00 1.490047e-01     1      0  1 -0.694122644
#> 360  82 1.490047e-01 2.579894e-01     1      0  1 -0.694122644
#> 361  82 2.579894e-01 2.997549e-01     1      0  1 -0.694122644
#> 362  82 2.997549e-01 4.186610e-01     1      0  1 -0.694122644
#> 363  82 4.186610e-01 7.240851e+00     0      1  1 -0.694122644
#> 364  83 0.000000e+00 1.391789e+01     1      0  1 -0.132297619
#> 365  83 1.391789e+01 6.000000e+01     0      0  1 -0.132297619
#> 366  84 0.000000e+00 3.530912e-01     1      0  0 -0.473649139
#> 367  84 3.530912e-01 1.334723e+00     1      0  0 -0.473649139
#> 368  84 1.334723e+00 1.984983e+00     1      0  0 -0.473649139
#> 369  84 1.984983e+00 3.076728e+00     1      0  0 -0.473649139
#> 370  84 3.076728e+00 6.471379e+00     1      0  0 -0.473649139
#> 371  84 6.471379e+00 6.952363e+00     1      0  0 -0.473649139
#> 372  84 6.952363e+00 1.312876e+01     1      0  0 -0.473649139
#> 373  84 1.312876e+01 2.641999e+01     1      0  0 -0.473649139
#> 374  84 2.641999e+01 3.920847e+01     1      0  0 -0.473649139
#> 375  84 3.920847e+01 4.008262e+01     0      0  0 -0.473649139
#> 376  85 0.000000e+00 1.612917e-01     1      0  0  0.369760664
#> 377  85 1.612917e-01 4.829317e-01     1      0  0  0.369760664
#> 378  85 4.829317e-01 1.270574e+00     1      0  0  0.369760664
#> 379  85 1.270574e+00 3.967454e+00     1      0  0  0.369760664
#> 380  85 3.967454e+00 4.010330e+00     1      0  0  0.369760664
#> 381  85 4.010330e+00 8.297516e+00     1      0  0  0.369760664
#> 382  85 8.297516e+00 4.105444e+01     1      0  0  0.369760664
#> 383  85 4.105444e+01 4.482648e+01     1      0  0  0.369760664
#> 384  85 4.482648e+01 4.611664e+01     1      0  0  0.369760664
#> 385  85 4.611664e+01 5.496999e+01     1      0  0  0.369760664
#> 386  85 5.496999e+01 6.000000e+01     0      0  0  0.369760664
#> 387  86 0.000000e+00 1.671088e+00     1      0  0  0.448389354
#> 388  86 1.671088e+00 3.832459e+00     1      0  0  0.448389354
#> 389  86 3.832459e+00 4.035030e+00     1      0  0  0.448389354
#> 390  86 4.035030e+00 5.836090e+00     1      0  0  0.448389354
#> 391  86 5.836090e+00 6.381097e+00     1      0  0  0.448389354
#> 392  86 6.381097e+00 6.746338e+00     0      1  0  0.448389354
#> 393  87 0.000000e+00 1.026519e-01     1      0  0 -0.173000444
#> 394  87 1.026519e-01 8.448658e-01     1      0  0 -0.173000444
#> 395  87 8.448658e-01 1.484730e+00     1      0  0 -0.173000444
#> 396  87 1.484730e+00 3.379099e+00     1      0  0 -0.173000444
#> 397  87 3.379099e+00 4.124874e+00     1      0  0 -0.173000444
#> 398  87 4.124874e+00 4.321140e+00     1      0  0 -0.173000444
#> 399  87 4.321140e+00 1.002313e+01     1      0  0 -0.173000444
#> 400  87 1.002313e+01 1.567652e+01     0      0  0 -0.173000444
#> 401  88 0.000000e+00 7.071221e-01     1      0  1 -0.891028534
#> 402  88 7.071221e-01 4.149804e+00     1      0  1 -0.891028534
#> 403  88 4.149804e+00 1.424293e+01     1      0  1 -0.891028534
#> 404  88 1.424293e+01 1.874865e+01     1      0  1 -0.891028534
#> 405  88 1.874865e+01 2.615463e+01     1      0  1 -0.891028534
#> 406  88 2.615463e+01 6.000000e+01     0      0  1 -0.891028534
#> 407  89 0.000000e+00 1.226071e+00     0      1  0  0.232470877
#> 408  90 0.000000e+00 3.354035e-04     1      0  0 -0.975515305
#> 409  90 3.354035e-04 2.135813e-01     1      0  0 -0.975515305
#> 410  90 2.135813e-01 2.749449e-01     1      0  0 -0.975515305
#> 411  90 2.749449e-01 4.342548e-01     1      0  0 -0.975515305
#> 412  90 4.342548e-01 5.956394e-01     1      0  0 -0.975515305
#> 413  90 5.956394e-01 1.962013e+00     1      0  0 -0.975515305
#> 414  90 1.962013e+00 3.746200e+00     1      0  0 -0.975515305
#> 415  90 3.746200e+00 8.077611e+00     1      0  0 -0.975515305
#> 416  90 8.077611e+00 9.601795e+00     1      0  0 -0.975515305
#> 417  90 9.601795e+00 1.605971e+01     1      0  0 -0.975515305
#> 418  90 1.605971e+01 4.680406e+01     1      0  0 -0.975515305
#> 419  90 4.680406e+01 4.795610e+01     1      0  0 -0.975515305
#> 420  90 4.795610e+01 5.603764e+01     0      0  0 -0.975515305
#> 421  91 0.000000e+00 1.719284e-01     1      0  0 -0.258056670
#> 422  91 1.719284e-01 8.099332e-01     1      0  0 -0.258056670
#> 423  91 8.099332e-01 1.560305e+00     1      0  0 -0.258056670
#> 424  91 1.560305e+00 1.628930e+00     1      0  0 -0.258056670
#> 425  91 1.628930e+00 2.255163e+00     1      0  0 -0.258056670
#> 426  91 2.255163e+00 2.292483e+00     1      0  0 -0.258056670
#> 427  91 2.292483e+00 2.481852e+00     1      0  0 -0.258056670
#> 428  91 2.481852e+00 3.361098e+00     1      0  0 -0.258056670
#> 429  91 3.361098e+00 1.701309e+01     1      0  0 -0.258056670
#> 430  91 1.701309e+01 2.058453e+01     1      0  0 -0.258056670
#> 431  91 2.058453e+01 2.884336e+01     1      0  0 -0.258056670
#> 432  91 2.884336e+01 3.590606e+01     1      0  0 -0.258056670
#> 433  91 3.590606e+01 3.769629e+01     1      0  0 -0.258056670
#> 434  91 3.769629e+01 4.209508e+01     1      0  0 -0.258056670
#> 435  91 4.209508e+01 6.000000e+01     0      0  0 -0.258056670
#> 436  92 0.000000e+00 8.550434e-01     1      0  0  0.244540159
#> 437  92 8.550434e-01 9.143162e-01     0      1  0  0.244540159
#> 438  93 0.000000e+00 7.368084e+00     0      1  1  0.451012363
#> 439  94 0.000000e+00 1.387448e+01     0      1  1  0.320181497
#> 440  95 0.000000e+00 2.699010e-01     1      0  0  0.475604439
#> 441  95 2.699010e-01 1.600107e+01     1      0  0  0.475604439
#> 442  95 1.600107e+01 2.125056e+01     1      0  0  0.475604439
#> 443  95 2.125056e+01 6.000000e+01     0      0  0  0.475604439
#> 444  96 0.000000e+00 7.175747e-01     0      1  1 -0.299561605
#> 445  97 0.000000e+00 1.790488e-01     1      0  0 -0.665347496
#> 446  97 1.790488e-01 5.636635e-01     1      0  0 -0.665347496
#> 447  97 5.636635e-01 1.351069e+00     1      0  0 -0.665347496
#> 448  97 1.351069e+00 4.147202e+00     1      0  0 -0.665347496
#> 449  97 4.147202e+00 4.861684e+00     1      0  0 -0.665347496
#> 450  97 4.861684e+00 6.465001e+00     1      0  0 -0.665347496
#> 451  97 6.465001e+00 6.654952e+00     1      0  0 -0.665347496
#> 452  97 6.654952e+00 7.324026e+00     1      0  0 -0.665347496
#> 453  97 7.324026e+00 9.072599e+00     1      0  0 -0.665347496
#> 454  97 9.072599e+00 1.195089e+01     0      1  0 -0.665347496
#> 455  98 0.000000e+00 2.214560e-02     1      0  0 -0.296104873
#> 456  98 2.214560e-02 5.998626e-01     1      0  0 -0.296104873
#> 457  98 5.998626e-01 1.259891e+00     1      0  0 -0.296104873
#> 458  98 1.259891e+00 1.574676e+00     1      0  0 -0.296104873
#> 459  98 1.574676e+00 2.465017e+00     1      0  0 -0.296104873
#> 460  98 2.465017e+00 4.421609e+00     1      0  0 -0.296104873
#> 461  98 4.421609e+00 4.857524e+00     1      0  0 -0.296104873
#> 462  98 4.857524e+00 9.015672e+00     1      0  0 -0.296104873
#> 463  98 9.015672e+00 2.054160e+01     1      0  0 -0.296104873
#> 464  98 2.054160e+01 2.068759e+01     1      0  0 -0.296104873
#> 465  98 2.068759e+01 2.562922e+01     1      0  0 -0.296104873
#> 466  98 2.562922e+01 3.883632e+01     1      0  0 -0.296104873
#> 467  98 3.883632e+01 6.000000e+01     0      0  0 -0.296104873
#> 468  99 0.000000e+00 1.340162e+00     0      1  0  0.900525428
#> 469 100 0.000000e+00 5.127804e-01     0      1  1  0.527669296