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 )
| n | number of observation. |
|---|---|
| summary | a logical value indicating whether a brief data summary will be printed. |
| para | a list of numerical vectors for the regression coefficients
in the joint scale-change model.
The names of the list elements are |
| xmat | an optional matrix specifying the design matrix. |
| censoring | a numeric variable specifying the censoring times for each of the \(n\) observation. |
| frailty | a numeric variable specifying the frailty variable. |
| tau | a numeric value specifying the maximum observation time. |
| origin | a numeric value specifying the time origin. |
| Lam0 | 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 $$\Lambda_0(t) = 2\log(1 + t).$$ |
| Haz0 | 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 $$H_0(t) = \log(1 + t) / 5.$$ |
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.
#> 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