Solari et al (2017) automatic GPD threshold selection
GPD_Threshold_Solari.RdAutomatic threshold selection method in Solari et al. (2017) is implemented to find the threshold above which excesses are follow a GPD. The code is based on the ANALISIS_POT_LNORM function provided by Sebastian Solari.
Arguments
- Event
Numeric vector containing the declustered events.
- Data
Original time series. Dataframe containing two columns. In column:
1A"Date"object of equally spaced discrete time steps.2Numeric vector containing corresponding time series values.
- RPs
Numeric vector specifying the return levels calculated from the GPD fits over the thresholds. Default is
c(50,100,500,100)plus the return period associated with the minimum candidate threshold.- RPs_PLOT
Numeric vector of length three specifying which elements of
RPsare plotted in the middle row of the graphical output. Default isc(1,2,3).- Min_Quantile
Numeric vector of length one specifying the minimum threshold, expressed as a quantile of the original time series (2nd column of
Data) to be tested. Default0.95.- Alpha
Numeric vector of length one specifying the level of confidence associated with the confidence interval i.e., the probability that the interval contains the true value of the parameter is \(1-\frac{Alpha}{2}\). The interval is referred to as the \(100(1-\frac{Alpha}{2})\%\) confidence interval. Default is
0.1.- mu
(average) occurrence frequency of events in the original time series
Data. Numeric vector of length one. Default is365.25, daily data.- N_Sim
Numeric vector of length one specifying the number of bootstrap samples. Default is
10.
Value
List comprising
Thres_CandidateThresholds tested which are the cluster maxima inEventsexceeding theMin_Quantilequantile of the original time series (given in column 2 ofData).GPD_MLEGPD parameter estimates, Mean Residual Life Plot (MRLP) values and return level estimates associated with eachThres_Candidate.CI_UpperUpper limits of the confidence interval for the point estimates of the corresponding element ofGPD_MLE.CI_LowerLower limits of the confidence interval for the point estimates of the corresponding element ofGPD_MLE.AR2Value of the right-tail weighted Anderson Darling statistic \(A_R^2\), the test statistic used in the Solari et al. (2017) method for eachThres_Candidate.AR2_pValuep-value associated with \(A_R^2\).
To interpret the graphical output. Top row: The GPD exhibits certain threshold stability properties. The guiding principle for threshold choice is to find the lowest value of the threshold such that the parameter estimates stabilize to a constant value which is sustained at all higher thresholds, once the sample uncertainty has been accounted for (typically assessed by pointwise uncertainty intervals). Mean residual life plot (left). If the GPD is a valid model for excesses above a threshold then the mean of these excesses will be a linear function of the threshold. We therefore select the lowest threshold where there is a linear trend in the mean residual life plot. Parameter stability plots for the shape (center) and scale (right) parameters. If the GPD is a suitable model for a threshold then for all higher thresholds it will also be suitable, with the shape and scale parameters being constant. The lowest threshold - to reduce the associated uncertainty - at which the parameter estimates are stable for all higher thresholds should be selected. Middle row: Return levels estimated from the GPD fitted at various thresholds. Lower row: Right-tail weighted Anderson Darling statistic \(A_R^2\) associated with the GPD fitted using various thresholds. Lower \(A_R^2\) statistic values signify less (quadratic) distance between the empirical distribution and the GPD i.e., GPD is a better fit for these thresholds (left). \(1-p_{value}\) associated with the \(A_R^2\) for each threshold. The \(A_R^2\) goodness of fit tests, tests the null hypothesis that the observations are from a GPD. At smaller \(1-p_{value}\) figure there is less chance of rejecting the null hypothesis i.e., the GPD is more suitable at these thresholds (center). Events per year at each threshold (right).
Details
EDF-statistics are goodness-of-fit statistics based on a comparison of the Empirical Distribution Function (EDF) \(F_n\) and a candidate parametric probability distribution \(F\) Stephens et al. (1974). Quadratic EDF test measure the distance between \(F\) and \(F_n\) by:$$n\int^{\infty}_{-\infty}=(F(x)-F_n(x))^2w(x) dx$$ where \(n\) is the number of elements in the original sample and \(w(x)\) is a weighting function. In the Cramer Von Misses statistic \(w(x)=1\), whereas the Anderson-Darling statistic \(A^2\), assigns more weight to the tails of the data by setting \(w(x)=\frac{1}{F(x)(1-F(x))}\). Under the null hypothesis that the sample \(x_1,\dots,x_n\) is from a GPD, the transformation \(z=F_1(x)\) a sample z uniformly distribution between \(0\) and \(1\). $$A^2=-\frac{1}{n}\sum_{i=1}^{n} \{(2i-1)[log(z_i)+log(1-z_{n+z-i})]\}-n$$ Sinclair et al. (1990) proposed the right-tail weighted Anderson Darling statistic \(A_R^2\) which allocates more weight to the upper tail and less to the lower tail of the distribution than \(A^2\) and is given by: $$A_R^2=\frac{n}{2}\sum_{i=1}^{n} \left [2-\frac{(2i-1)}{n}log(1-z_i)+2z_{i} \right]$$
Solari et al. (2017) formalized EDF statistic - GOF test threshold selection procedures used to test the null hypothesis that a sample is from a GPD distribution. creating an automated approach adopting the \(A_R^2\) as the EDF statistic. The authors also proposed combining the approach with a bootstrapping technique to assess the influence of threshold on the uncertainly of higher return period quantiles. The approach in Solari et al. (2017) comprises the following steps:
Decluster the time series to produce a series of \(n_p\) independent cluster maxima \(\{x_i:i=1,\dots,n_p\}\) and sort such that \(\{x_1\leq\dots\leq x_p\}\).
The sorted series defines a series of \(n_u\) thresholds after excluding repeated values i.e., \(n_u \leq n_p\). For each threshold \(\{u_j, j=1,\dots,n_u\}\) fit the GPD via L-Moments using only the excesses satisfying \(x>u_j\). Then, calculate the R-AD statistic and its associated p-value for each threshold.
Select the threshold that minimizes one minus the p-value i.e., $$u_0 = argmin_{u_j} (1-p(u_j)).$$
Examples
#Declustering the rainfall at site S22 using a 7-day window.
Rainfall_Declust_SW<-Decluster_SW(Data=S22.Detrend.df[,c(1:2)],Window_Width=7)
#> Warning: no non-missing arguments to max; returning -Inf
#> Warning: no non-missing arguments to max; returning -Inf
#> Warning: no non-missing arguments to max; returning -Inf
#> Warning: no non-missing arguments to max; returning -Inf
#> Warning: no non-missing arguments to max; returning -Inf
#Finding an appropriate threshold for the declustered series
GPD_Threshold_Solari(Event=Rainfall_Declust_SW$Declustered,
Data=S22.Detrend.df[,2],
Min_Quantile = 0.99)
#> Fitted values of xi < -0.5
#> $Thres_Candidate
#> [1] 2.37 2.38 2.39 2.40 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.50 2.52
#> [16] 2.53 2.54 2.55 2.56 2.57 2.58 2.60 2.61 2.62 2.63 2.64 2.65 2.66 2.67 2.69
#> [31] 2.70 2.72 2.73 2.75 2.76 2.78 2.80 2.82 2.84 2.85 2.86 2.87 2.88 2.89 2.90
#> [46] 2.91 2.92 2.94 2.95 2.97 3.00 3.02 3.04 3.05 3.06 3.07 3.08 3.09 3.12 3.13
#> [61] 3.14 3.15 3.16 3.17 3.19 3.20 3.22 3.23 3.25 3.28 3.30 3.31 3.35 3.37 3.41
#> [76] 3.42 3.45 3.48 3.49 3.54 3.57 3.59 3.60 3.63 3.70 3.72 3.73 3.74 3.75 3.79
#> [91] 3.83 3.90 3.93 3.94 4.01 4.02 4.03 4.07 4.12 4.15 4.18 4.20 4.22 4.29 4.33
#> [106] 4.36 4.38 4.39 4.42 4.51 4.54 4.60 4.63 4.67 4.71 4.74 4.85
#>
#> $Thres_Candidate_Quantile
#> [1] 0.9902153 0.9902153 0.9902153 0.9902153 0.9903694 0.9903694 0.9904850
#> [8] 0.9904850 0.9906391 0.9906391 0.9906391 0.9906391 0.9906776 0.9907932
#> [15] 0.9907932 0.9907932 0.9908702 0.9908702 0.9909858 0.9909858 0.9909858
#> [22] 0.9911399 0.9911399 0.9911399 0.9911399 0.9912554 0.9912554 0.9912554
#> [29] 0.9913325 0.9914095 0.9915636 0.9915636 0.9915636 0.9915636 0.9916407
#> [36] 0.9916792 0.9918333 0.9918333 0.9918333 0.9918333 0.9919488 0.9919488
#> [43] 0.9919488 0.9921029 0.9921029 0.9921029 0.9921029 0.9922185 0.9922185
#> [50] 0.9922955 0.9922955 0.9923726 0.9923726 0.9924496 0.9924496 0.9925652
#> [57] 0.9926808 0.9926808 0.9927578 0.9927578 0.9928349 0.9928349 0.9928734
#> [64] 0.9929889 0.9929889 0.9930275 0.9930660 0.9931430 0.9931430 0.9932586
#> [71] 0.9932586 0.9932586 0.9933356 0.9933356 0.9935283 0.9935283 0.9935283
#> [78] 0.9935283 0.9935283 0.9936053 0.9936053 0.9936438 0.9937594 0.9937594
#> [85] 0.9937594 0.9938750 0.9938750 0.9939135 0.9940290 0.9940290 0.9940290
#> [92] 0.9941831 0.9941831 0.9941831 0.9942217 0.9942987 0.9942987 0.9944143
#> [99] 0.9944143 0.9944143 0.9945684 0.9945684 0.9945684 0.9945684 0.9946069
#> [106] 0.9947224 0.9948380 0.9948380 0.9949151 0.9949151 0.9949536 0.9950691
#> [113] 0.9950691 0.9951462 0.9951462 0.9951847 0.9952232 0.9952618 0.9954158
#> [120] 0.9954158 0.9954158 0.9954158 0.9954544 0.9954929 0.9955314 0.9956085
#> [127] 0.9956085 0.9956470 0.9956855 0.9957625 0.9957625 0.9958396 0.9958396
#> [134] 0.9958781 0.9959166 0.9959552 0.9960322 0.9961478 0.9961478 0.9961478
#> [141] 0.9962248 0.9962248 0.9962633 0.9963019 0.9964174 0.9964174 0.9964174
#> [148] 0.9964945 0.9965715 0.9965715 0.9966486 0.9966486 0.9968027 0.9968027
#> [155] 0.9968027 0.9968027 0.9969182 0.9969182 0.9969567 0.9970338 0.9970723
#> [162] 0.9971108 0.9971494 0.9971879 0.9972264 0.9972649 0.9973034 0.9973420
#> [169] 0.9973805 0.9974190 0.9974575 0.9974961 0.9976116 0.9976116 0.9976887
#> [176] 0.9976887 0.9977657 0.9978042 0.9978428 0.9978813 0.9979198 0.9979968
#> [183] 0.9979968 0.9980739 0.9980739 0.9981124 0.9981509 0.9981895 0.9982280
#> [190] 0.9982665 0.9983050 0.9983435 0.9984206 0.9984206 0.9984591 0.9984976
#> [197] 0.9985362 0.9986132 0.9986902 0.9986902 0.9987288 0.9987673 0.9988058
#> [204] 0.9988443 0.9988829 0.9989599 0.9989599 0.9989984 0.9990369 0.9990755
#> [211] 0.9991140 0.9991525 0.9991910 0.9992296 0.9992681 0.9993066 0.9993451
#> [218] 0.9993836 0.9994222 0.9994607 0.9994992 0.9995377 0.9995763 0.9996148
#> [225] 0.9996533 0.9996918 0.9997303 0.9997689 0.9998074 0.9998459 0.9998844
#> [232] 0.9999230 0.9999615 1.0000000
#>
#> $GPD_MLE
#> xi sigma u MRLP mod_sigma rate 10
#> [1,] 0.29119653 0.9188936 2.38 1.270174 0.22584590 3.2361609 7.909916
#> [2,] 0.29420830 0.9167146 2.39 1.271316 0.21355675 3.2080203 7.918368
#> [3,] 0.28457675 0.9366356 2.40 1.272566 0.25365135 3.1798798 7.917586
#> [4,] 0.29356622 0.9235429 2.41 1.285495 0.21604828 3.1235988 7.904405
#> [5,] 0.28967461 0.9334550 2.42 1.281312 0.23244248 3.1095285 7.918823
#> [6,] 0.29194156 0.9326553 2.43 1.288945 0.22323733 3.0673177 7.914380
#> [7,] 0.28767434 0.9433958 2.44 1.290880 0.24147037 3.0391772 7.917376
#> [8,] 0.27596988 0.9674947 2.45 1.299061 0.29136849 2.9969664 7.904173
#> [9,] 0.27005141 0.9813841 2.46 1.313923 0.31705765 2.9406853 7.882202
#> [10,] 0.27827527 0.9690193 2.47 1.323058 0.28167935 2.8984745 7.874526
#> [11,] 0.28569692 0.9579977 2.48 1.319512 0.24946929 2.8844043 7.888586
#> [12,] 0.27300485 0.9850494 2.49 1.315980 0.30526728 2.8703340 7.903979
#> [13,] 0.28052548 0.9737522 2.50 1.332300 0.27243855 2.8140529 7.881019
#> [14,] 0.30314415 0.9383576 2.52 1.318995 0.17443428 2.7999827 7.924523
#> [15,] 0.28931006 0.9667671 2.53 1.315657 0.23481263 2.7859124 7.938247
#> [16,] 0.28198612 0.9830392 2.54 1.332784 0.26679441 2.7296313 7.911238
#> [17,] 0.26719393 1.0149148 2.55 1.343717 0.33357025 2.6874205 7.903512
#> [18,] 0.26568619 1.0199291 2.56 1.362460 0.33977243 2.6311395 7.873101
#> [19,] 0.26428337 1.0254903 2.57 1.367189 0.34628210 2.6029990 7.871958
#> [20,] 0.26309345 1.0306847 2.58 1.372131 0.35190364 2.5748584 7.870661
#> [21,] 0.27492694 1.0130106 2.60 1.367293 0.29820061 2.5467179 7.888368
#> [22,] 0.28116819 1.0041031 2.61 1.372570 0.27025417 2.5185774 7.885336
#> [23,] 0.27932401 1.0103661 2.62 1.370281 0.27853716 2.5045071 7.896204
#> [24,] 0.27736201 1.0171274 2.63 1.375852 0.28766536 2.4763666 7.894256
#> [25,] 0.27497111 1.0243092 2.64 1.381667 0.29838545 2.4482260 7.889922
#> [26,] 0.28101162 1.0158433 2.65 1.387733 0.27116246 2.4200855 7.885694
#> [27,] 0.27835663 1.0241839 2.66 1.385848 0.28375521 2.4060153 7.898656
#> [28,] 0.28396991 1.0160463 2.67 1.392249 0.25784667 2.3778747 7.891077
#> [29,] 0.30508264 0.9822649 2.69 1.380536 0.16159258 2.3638045 7.920710
#> [30,] 0.30243392 0.9906526 2.70 1.378802 0.17408105 2.3497342 7.934476
#> [31,] 0.30584817 0.9906334 2.72 1.375515 0.15872639 2.3215937 7.955845
#> [32,] 0.30239587 0.9999535 2.73 1.390988 0.17441276 2.2793829 7.934655
#> [33,] 0.28534269 1.0388393 2.75 1.388375 0.25414689 2.2512423 7.962225
#> [34,] 0.28027119 1.0515225 2.76 1.423161 0.27797401 2.1808910 7.908824
#> [35,] 0.29982863 1.0196095 2.78 1.421765 0.18608589 2.1527505 7.914888
#> [36,] 0.30045653 1.0254651 2.80 1.411118 0.18418679 2.1386802 7.953217
#> [37,] 0.31071758 1.0128369 2.82 1.419530 0.13661335 2.0964694 7.950744
#> [38,] 0.33307507 0.9793407 2.84 1.418844 0.03340747 2.0683289 7.964466
#> [39,] 0.31540245 1.0143138 2.85 1.418562 0.11541678 2.0542586 7.977058
#> [40,] 0.29699554 1.0516510 2.86 1.438322 0.20224379 2.0120478 7.954713
#> [41,] 0.30078515 1.0477038 2.87 1.459143 0.18445044 1.9698371 7.924208
#> [42,] 0.29325037 1.0652775 2.88 1.459640 0.22071642 1.9557668 7.935016
#> [43,] 0.27310824 1.1078083 2.89 1.470949 0.31852550 1.9276263 7.934514
#> [44,] 0.24230680 1.1763410 2.90 1.493881 0.47365131 1.8854155 7.935495
#> [45,] 0.24370805 1.1759878 2.91 1.529846 0.46679740 1.8291344 7.882941
#> [46,] 0.24480943 1.1759073 2.92 1.531705 0.46106377 1.8150641 7.883021
#> [47,] 0.24707626 1.1761952 2.94 1.523672 0.44979097 1.8009939 7.903785
#> [48,] 0.23645611 1.2024627 2.95 1.537857 0.50491717 1.7728533 7.901034
#> [49,] 0.24908109 1.1793320 2.97 1.542661 0.43956121 1.7447128 7.886557
#> [50,] 0.26347199 1.1563494 3.00 1.525203 0.36593343 1.7306426 7.913352
#> [51,] 0.26513074 1.1584014 3.02 1.530413 0.35770657 1.7025020 7.914821
#> [52,] 0.27952844 1.1341601 3.04 1.536134 0.28439369 1.6743615 7.902270
#> [53,] 0.28019398 1.1356831 3.05 1.539153 0.28109143 1.6602912 7.902878
#> [54,] 0.28074559 1.1374873 3.06 1.542308 0.27840579 1.6462210 7.903566
#> [55,] 0.24050901 1.2271076 3.07 1.545603 0.48874492 1.6321507 7.954781
#> [56,] 0.23913023 1.2323624 3.08 1.590804 0.49584131 1.5758696 7.891250
#> [57,] 0.23802361 1.2378784 3.09 1.595135 0.50238540 1.5617994 7.893237
#> [58,] 0.26177994 1.1921660 3.12 1.579636 0.37541256 1.5477291 7.894999
#> [59,] 0.24630467 1.2292287 3.13 1.584128 0.45829507 1.5336588 7.916428
#> [60,] 0.24471908 1.2353432 3.14 1.603738 0.46692528 1.5055183 7.894160
#> [61,] 0.24262154 1.2427216 3.15 1.608868 0.47846374 1.4914481 7.894987
#> [62,] 0.22618427 1.2832852 3.16 1.614190 0.56854287 1.4773778 7.918704
#> [63,] 0.20979032 1.3254898 3.17 1.635534 0.66045449 1.4492373 7.922833
#> [64,] 0.21744481 1.3111725 3.19 1.647921 0.61752353 1.4210967 7.898570
#> [65,] 0.21418710 1.3218879 3.20 1.654400 0.63648918 1.4070265 7.901436
#> [66,] 0.22158302 1.3078519 3.22 1.651111 0.59435458 1.3929562 7.898019
#> [67,] 0.21774829 1.3192285 3.23 1.657959 0.61590156 1.3788859 7.898926
#> [68,] 0.19624612 1.3794080 3.25 1.655052 0.74160813 1.3648157 7.960420
#> [69,] 0.19718740 1.3833855 3.28 1.677872 0.73661079 1.3226049 7.937774
#> [70,] 0.20193050 1.3744400 3.30 1.694348 0.70806939 1.2944643 7.908838
#> [71,] 0.19695147 1.3898582 3.31 1.702967 0.73794887 1.2803941 7.913296
#> [72,] 0.19149951 1.4132926 3.35 1.681889 0.77176924 1.2663238 7.970415
#> [73,] 0.19516537 1.4076040 3.37 1.719885 0.74989673 1.2241130 7.916971
#> [74,] 0.20307921 1.3950907 3.41 1.699884 0.70259063 1.2100428 7.938382
#> [75,] 0.18030499 1.4583844 3.42 1.730357 0.84174131 1.1819022 7.957287
#> [76,] 0.14394184 1.5704663 3.45 1.742561 1.07386696 1.1537617 8.053604
#> [77,] 0.13627341 1.5995482 3.48 1.801923 1.12531669 1.0974806 8.011355
#> [78,] 0.12825099 1.6261993 3.49 1.839342 1.17860331 1.0693401 7.993149
#> [79,] 0.15001383 1.5656074 3.54 1.813867 1.03455847 1.0552698 7.965340
#> [80,] 0.15751428 1.5484183 3.57 1.808378 0.98609232 1.0411996 7.957860
#> [81,] 0.15660645 1.5542852 3.59 1.813151 0.99206809 1.0271293 7.959029
#> [82,] 0.14732134 1.5836474 3.60 1.828333 1.05329063 1.0130591 7.970126
#> [83,] 0.15377233 1.5696976 3.63 1.824085 1.01150407 0.9989888 7.964684
#> [84,] 0.19614199 1.4599601 3.70 1.780143 0.73423471 0.9849185 7.914452
#> [85,] 0.19554779 1.4666204 3.72 1.785942 0.73918264 0.9708483 7.917628
#> [86,] 0.18422881 1.4990342 3.73 1.802206 0.81186076 0.9567780 7.928435
#> [87,] 0.17311219 1.5326270 3.74 1.819104 0.88518740 0.9427077 7.941881
#> [88,] 0.16178452 1.5678534 3.75 1.836667 0.96116139 0.9286375 7.956961
#> [89,] 0.17627722 1.5331089 3.79 1.824923 0.86501818 0.9145672 7.940312
#> [90,] 0.19104117 1.4984825 3.83 1.813437 0.76679484 0.9004969 7.922543
#> [91,] 0.24170872 1.3836615 3.90 1.772222 0.44099746 0.8864267 7.875932
#> [92,] 0.22478995 1.4332776 3.93 1.770806 0.54985312 0.8723564 7.929495
#> [93,] 0.18427375 1.5439797 3.94 1.819833 0.81794116 0.8442159 7.974913
#> [94,] 0.23100967 1.4350029 4.01 1.812586 0.50865408 0.8160753 7.886964
#> [95,] 0.21376294 1.4817892 4.02 1.834386 0.62246217 0.8020051 7.905739
#> [96,] 0.19673576 1.5301562 4.03 1.857143 0.73731103 0.7879348 7.926397
#> [97,] 0.20990953 1.5027781 4.07 1.850909 0.64844630 0.7738646 7.911064
#> [98,] 0.23608460 1.4475867 4.12 1.835185 0.47491811 0.7597943 7.885177
#> [99,] 0.20701683 1.5302408 4.15 1.839811 0.67112093 0.7457240 7.962633
#> [100,] 0.17580143 1.6234312 4.18 1.881961 0.88858124 0.7175835 8.003493
#> [101,] 0.16380291 1.6626610 4.20 1.938776 0.97468873 0.6894430 7.975759
#> [102,] 0.15071486 1.7053254 4.22 1.959167 1.06930869 0.6753727 7.994618
#> [103,] 0.18322614 1.6226182 4.29 1.930851 0.83657808 0.6613024 7.952544
#> [104,] 0.18842591 1.6154179 4.33 1.932826 0.79953367 0.6472322 7.945800
#> [105,] 0.18291952 1.6376497 4.36 1.945778 0.84012059 0.6331619 7.955132
#> [106,] 0.16582199 1.6903250 4.38 1.970000 0.96402462 0.6190916 7.978109
#> [107,] 0.13928105 1.7733440 4.39 2.005814 1.16190016 0.6050214 8.018005
#> [108,] 0.09527877 1.9249419 4.42 2.023571 1.50380975 0.5909511 8.146257
#> [109,] 0.12877069 1.8232961 4.51 2.034750 1.24254028 0.5628106 8.038187
#> [110,] 0.11558420 1.8714064 4.54 2.056923 1.34665414 0.5487403 8.061063
#> [111,] 0.12478425 1.8485752 4.60 2.051053 1.27456765 0.5346701 8.047100
#> [112,] 0.10898941 1.9053943 4.63 2.076486 1.40077327 0.5205998 8.073894
#> [113,] 0.05994506 2.0853601 4.67 2.094167 1.80541666 0.5065295 8.223303
#> [114,] 0.04662777 2.1397128 4.71 2.177353 1.92009603 0.4783890 8.184442
#> [115,] 0.02572465 2.2243882 4.74 2.213333 2.10245333 0.4643187 8.223674
#> [116,] 0.05189567 2.1268609 4.85 2.172500 1.87516686 0.4502485 8.178393
#> [117,] 0.01534926 2.2718339 4.86 2.232581 2.19723648 0.4361782 8.244251
#> 50 100 500 1000
#> [1,] 13.10259 16.20651 26.35935 32.42821
#> [2,] 13.15349 16.29317 26.60024 32.78173
#> [3,] 13.03488 16.07153 25.92564 31.77316
#> [4,] 13.12284 16.25031 26.50935 32.65769
#> [5,] 13.09878 16.18992 26.28247 32.30519
#> [6,] 13.11984 16.23395 26.42926 32.52850
#> [7,] 13.07357 16.14375 26.14383 32.09824
#> [8,] 12.91436 15.85938 25.31791 30.87769
#> [9,] 12.81237 15.69149 24.87298 30.23478
#> [10,] 12.89528 15.85402 25.38295 30.99838
#> [11,] 13.00350 16.04248 25.91743 31.78456
#> [12,] 12.88197 15.79850 25.13231 30.60086
#> [13,] 12.93251 15.91675 25.55381 31.24706
#> [14,] 13.26995 16.50742 27.25045 33.75698
#> [15,] 13.12703 16.22219 26.32345 32.34895
#> [16,] 12.99842 16.00859 25.74645 31.50851
#> [17,] 12.82091 15.68352 24.78117 30.07727
#> [18,] 12.75641 15.59444 24.59771 29.83015
#> [19,] 12.73966 15.56425 24.50981 29.70066
#> [20,] 12.72519 15.53843 24.43536 29.59121
#> [21,] 12.88239 15.81453 25.21992 30.74212
#> [22,] 12.94797 15.94092 25.61354 31.33185
#> [23,] 12.94421 15.92246 25.52629 31.19239
#> [24,] 12.91970 15.87823 25.39603 30.99925
#> [25,] 12.88608 15.81961 25.22999 30.75538
#> [26,] 12.94718 15.93893 25.60589 31.31985
#> [27,] 12.93892 15.90942 25.47717 31.11597
#> [28,] 12.98908 16.01227 25.81552 31.62898
#> [29,] 13.27798 16.52954 27.34453 33.90861
#> [30,] 13.27044 16.49966 27.20615 33.68550
#> [31,] 13.34568 16.61975 27.51968 34.14088
#> [32,] 13.27062 16.49970 27.20525 33.68376
#> [33,] 13.12234 16.18698 26.14107 32.05291
#> [34,] 12.98223 15.97859 25.65180 31.36481
#> [35,] 13.20871 16.40326 26.96165 33.33311
#> [36,] 13.28011 16.49685 27.13659 33.56157
#> [37,] 13.39490 16.71969 27.85361 34.65318
#> [38,] 13.68452 17.26438 29.58055 37.28853
#> [39,] 13.49456 16.88149 28.28780 35.28959
#> [40,] 13.24699 16.43069 26.91738 33.22589
#> [41,] 13.24052 16.45202 27.07865 33.49804
#> [42,] 13.17496 16.31421 26.60803 32.77507
#> [43,] 12.95825 15.90193 25.32376 30.84451
#> [44,] 12.65263 15.32407 23.56517 28.23232
#> [45,] 12.58891 15.25817 23.50633 28.18474
#> [46,] 12.59929 15.27766 23.56486 28.27116
#> [47,] 12.65241 15.35594 23.74366 28.51903
#> [48,] 12.54894 15.16415 23.17564 27.68341
#> [49,] 12.64598 15.36168 23.80738 28.62644
#> [50,] 12.82610 15.67428 24.68577 29.91019
#> [51,] 12.84522 15.70886 24.78732 30.06023
#> [52,] 12.96980 15.96024 25.60575 31.29773
#> [53,] 12.97766 15.97457 25.64868 31.36172
#> [54,] 12.98456 15.98697 25.68525 31.41605
#> [55,] 12.67540 15.34348 23.55660 28.19863
#> [56,] 12.56888 15.20862 23.32114 27.89931
#> [57,] 12.56307 15.19518 23.27357 27.82689
#> [58,] 12.78315 15.61177 24.54328 29.71165
#> [59,] 12.67281 15.37844 23.76496 28.53556
#> [60,] 12.62560 15.31231 23.62444 28.34442
#> [61,] 12.60844 15.27872 23.51935 28.18786
#> [62,] 12.49972 15.04804 22.75966 27.04947
#> [63,] 12.36941 14.79822 22.00625 25.94342
#> [64,] 12.39817 14.87699 22.30065 26.39033
#> [65,] 12.37675 14.83327 22.16170 26.18429
#> [66,] 12.43168 14.94079 22.49226 26.67155
#> [67,] 12.40133 14.88253 22.31602 26.41250
#> [68,] 12.32065 14.66658 21.51761 25.20366
#> [69,] 12.29775 14.64601 21.51151 25.20922
#> [70,] 12.29259 14.66619 21.64493 25.42359
#> [71,] 12.26226 14.60397 21.44841 25.13381
#> [72,] 12.30240 14.62080 21.35346 24.95666
#> [73,] 12.25659 14.58860 21.39029 25.04537
#> [74,] 12.34470 14.73357 21.76680 25.57985
#> [75,] 12.20813 14.45479 20.89322 24.29607
#> [76,] 12.09808 14.15015 19.78399 22.64247
#> [77,] 12.00110 14.00800 19.46833 22.21495
#> [78,] 11.93251 13.89621 19.18890 21.82721
#> [79,] 12.02377 14.09704 19.82991 22.75858
#> [80,] 12.06037 14.17392 20.07001 23.10758
#> [81,] 12.05647 14.16525 20.04175 23.06614
#> [82,] 12.01577 14.07626 19.75575 22.64838
#> [83,] 12.04829 14.14327 19.96184 22.94689
#> [84,] 12.24171 14.56963 21.36723 25.02410
#> [85,] 12.24435 14.57044 21.35789 25.00689
#> [86,] 12.18593 14.44602 20.95306 24.40731
#> [87,] 12.13649 14.33564 20.58453 23.86071
#> [88,] 12.09057 14.23038 20.22987 23.33556
#> [89,] 12.15484 14.37229 20.69680 24.02440
#> [90,] 12.21936 14.51776 21.18872 24.75707
#> [91,] 12.48875 15.09937 23.14713 27.70176
#> [92,] 12.45211 14.96405 22.55297 26.76798
#> [93,] 12.26068 14.53588 21.08680 24.56452
#> [94,] 12.43034 14.97131 22.70502 27.03026
#> [95,] 12.34782 14.78494 22.05186 26.03880
#> [96,] 12.27501 14.61597 21.45644 25.13883
#> [97,] 12.33218 14.74741 21.91612 25.83234
#> [98,] 12.45980 15.03270 22.91113 27.34219
#> [99,] 12.39289 14.80531 21.94116 25.82687
#> [100,] 12.27380 14.51940 20.92059 24.28675
#> [101,] 12.17654 14.35605 20.48143 23.65949
#> [102,] 12.13693 14.25473 20.11554 23.11194
#> [103,] 12.24609 14.52277 21.06977 24.54135
#> [104,] 12.26396 14.56704 21.23088 24.78502
#> [105,] 12.25052 14.52739 21.07258 24.54200
#> [106,] 12.19678 14.39053 20.57066 23.78439
#> [107,] 12.12892 14.20379 19.86905 22.72842
#> [108,] 12.11203 14.01650 18.95513 21.32679
#> [109,] 12.11139 14.14300 19.62208 22.35490
#> [110,] 12.09122 14.07164 19.33068 21.91496
#> [111,] 12.10877 14.12553 19.53917 22.22722
#> [112,] 12.08623 14.04322 19.20010 21.71534
#> [113,] 12.10669 13.89812 18.35628 20.41285
#> [114,] 12.03146 13.77932 18.06235 20.00831
#> [115,] 12.02609 13.71283 17.74728 19.53695
#> [116,] 12.03840 13.80274 18.15268 20.14097
#> [117,] 12.03081 13.69063 17.61341 19.33294
#>
#> $CI_Upper
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 0.3715896 1.111980 2.3855 1.418520 0.7399105 3.2361609 8.789748
#> [2,] 0.3855604 1.049893 2.3955 1.403851 0.6213962 3.2080203 8.685930
#> [3,] 0.3403507 1.045873 2.4000 1.436387 0.5830544 3.1798798 8.918647
#> [4,] 0.4675734 1.076739 2.4210 1.517182 0.5186262 3.1235988 9.725970
#> [5,] 0.3780414 0.955207 2.4200 1.428398 0.4422533 3.1095285 9.002333
#> [6,] 0.3892930 1.051021 2.4400 1.556353 0.5328185 3.0673177 9.530561
#> [7,] 0.3109143 1.085879 2.4400 1.455949 0.5632195 3.0391772 8.589133
#> [8,] 0.3812295 1.073855 2.4500 1.356634 0.5896464 2.9969664 8.555494
#> [9,] 0.3215095 1.278172 2.4655 1.528275 0.9531848 2.9406853 8.523500
#> [10,] 0.3563199 1.077341 2.4800 1.365728 0.6375537 2.8984745 8.388958
#> [11,] 0.3762825 1.231168 2.4900 1.391588 0.9089025 2.8844043 8.043702
#> [12,] 0.3604240 1.047811 2.4900 1.523703 0.6082350 2.8703340 9.178052
#> [13,] 0.3886243 1.235100 2.5200 1.500643 0.8123698 2.8140529 8.300983
#> [14,] 0.4169633 1.196295 2.5300 1.640211 0.4700161 2.7999827 9.537089
#> [15,] 0.3846413 1.237797 2.5300 1.521093 0.8319509 2.7859124 9.259919
#> [16,] 0.4514163 1.124214 2.5400 1.607299 0.6025423 2.7296313 9.656478
#> [17,] 0.3417970 1.177761 2.5500 1.507861 0.7519987 2.6874205 8.714890
#> [18,] 0.3889379 1.169676 2.5655 1.688757 0.8337716 2.6311395 9.648883
#> [19,] 0.3911995 1.321361 2.5755 1.421495 1.2308530 2.6029990 8.469302
#> [20,] 0.4204860 1.128513 2.6110 1.589093 0.6559781 2.5748584 9.149377
#> [21,] 0.4049254 1.182397 2.6055 1.522528 0.8005203 2.5467179 8.736862
#> [22,] 0.2900556 1.249488 2.6200 1.600165 0.7024213 2.5185774 8.700864
#> [23,] 0.3621084 1.194330 2.6255 1.601576 0.6322473 2.5045071 9.137869
#> [24,] 0.4132065 1.220247 2.6400 1.539818 0.7516786 2.4763666 8.733758
#> [25,] 0.3827554 1.137288 2.6510 1.580859 0.6123374 2.4482260 8.883121
#> [26,] 0.4382998 1.060098 2.6600 1.646183 0.4517212 2.4200855 9.515390
#> [27,] 0.4111046 1.105092 2.6955 1.573363 0.7305326 2.4060153 9.027219
#> [28,] 0.3705208 1.250528 2.6900 1.583683 0.7807702 2.3778747 8.809336
#> [29,] 0.3721873 1.220770 2.7110 1.692982 0.7856610 2.3638045 9.270245
#> [30,] 0.4990816 1.112439 2.7200 1.638596 0.5812654 2.3497342 9.802706
#> [31,] 0.3142333 1.277386 2.7200 1.552106 0.7865526 2.3215937 8.497582
#> [32,] 0.3342011 1.242158 2.7500 1.653519 0.7304112 2.2793829 8.965682
#> [33,] 0.4122149 1.272576 2.7500 1.533984 0.7834416 2.2512423 8.453999
#> [34,] 0.4515062 1.167232 2.7820 1.508194 0.6962767 2.1808910 8.454728
#> [35,] 0.3970705 1.237698 2.8000 1.616856 0.9635445 2.1527505 8.657010
#> [36,] 0.3774981 1.302668 2.8110 1.775378 0.7371859 2.1386802 9.403317
#> [37,] 0.4387926 1.126967 2.8400 1.567919 0.7586612 2.0964694 8.657832
#> [38,] 0.4910278 1.209373 2.8500 1.573024 0.6460532 2.0683289 8.979615
#> [39,] 0.4128393 1.167461 2.8500 1.586106 0.7774783 2.0542586 8.775593
#> [40,] 0.3293490 1.363820 2.8600 1.627409 1.0516193 2.0120478 8.744981
#> [41,] 0.3715904 1.463466 2.8855 1.711646 1.0368268 1.9698371 8.493493
#> [42,] 0.3232211 1.457139 2.8800 1.701831 1.0227543 1.9557668 8.485374
#> [43,] 0.4444454 1.439172 2.8900 1.663931 1.1719715 1.9276263 8.658888
#> [44,] 0.3880208 1.360816 2.9055 1.828022 0.9536134 1.8854155 9.340131
#> [45,] 0.3417949 1.524595 2.9455 1.794988 1.2028921 1.8291344 8.797387
#> [46,] 0.3436782 1.662278 2.9310 1.768570 1.5114035 1.8150641 8.524220
#> [47,] 0.3688634 1.382566 2.9455 1.799738 0.7559274 1.8009939 9.071314
#> [48,] 0.3626740 1.373175 2.9610 1.756325 0.8304089 1.7728533 8.772991
#> [49,] 0.3983998 1.383808 3.0000 1.815165 1.0794057 1.7447128 9.105438
#> [50,] 0.3822965 1.411656 3.0110 1.673085 1.0892775 1.7306426 8.426388
#> [51,] 0.3058765 1.364263 3.0565 1.775508 0.8504571 1.7025020 8.735372
#> [52,] 0.3631977 1.588290 3.0655 1.804126 1.2759014 1.6743615 8.605675
#> [53,] 0.4214018 1.376174 3.0655 1.719356 0.9417915 1.6602912 8.545522
#> [54,] 0.3673272 1.499178 3.0700 1.752188 0.9762366 1.6462210 8.620551
#> [55,] 0.4293332 1.332386 3.0700 1.718461 0.7744957 1.6321507 8.807491
#> [56,] 0.3586846 1.636690 3.1300 1.863183 1.6108478 1.5758696 8.947724
#> [57,] 0.4213875 1.493258 3.1300 1.727806 1.3316827 1.5617994 8.336861
#> [58,] 0.2672750 1.532725 3.1355 1.910636 1.0652634 1.5477291 8.794008
#> [59,] 0.3640725 1.514332 3.1355 1.645693 1.3786483 1.5336588 8.158469
#> [60,] 0.5127783 1.488579 3.1555 2.135215 1.3655626 1.5055183 9.902776
#> [61,] 0.3208656 1.668406 3.1600 2.057741 1.3104450 1.4914481 9.483618
#> [62,] 0.3520031 1.488801 3.1700 1.879005 0.9404455 1.4773778 8.732314
#> [63,] 0.3688362 1.614471 3.1955 1.683689 1.6897092 1.4492373 7.989454
#> [64,] 0.3883783 1.656580 3.2110 2.020807 1.3354483 1.4210967 9.177453
#> [65,] 0.4378495 1.834175 3.2365 2.089910 1.5550098 1.4070265 9.178624
#> [66,] 0.3793386 1.654723 3.2410 1.834884 1.7165535 1.3929562 8.449552
#> [67,] 0.3362558 1.680546 3.2500 1.912306 1.2718644 1.3788859 8.545225
#> [68,] 0.3098925 1.562216 3.2665 1.919825 1.3064300 1.3648157 8.921767
#> [69,] 0.3746814 1.785711 3.2800 1.945729 2.0173196 1.3226049 8.722044
#> [70,] 0.2829979 1.703325 3.3055 1.841668 1.6243867 1.2944643 8.185074
#> [71,] 0.3252244 1.599698 3.3500 2.030242 1.1293231 1.2803941 8.902031
#> [72,] 0.2370334 1.624066 3.3830 1.908439 2.1770969 1.2663238 8.680850
#> [73,] 0.2917026 1.742615 3.4100 1.851247 1.8629048 1.2241130 8.511473
#> [74,] 0.3694391 1.735493 3.4100 2.011878 1.4383362 1.2100428 8.738777
#> [75,] 0.2635500 1.821821 3.4500 1.946833 1.7110347 1.1819022 8.536980
#> [76,] 0.3342795 1.934734 3.4500 2.079982 2.2112129 1.1537617 9.026290
#> [77,] 0.2345960 1.940743 3.4800 2.084218 2.0329924 1.0974806 8.786132
#> [78,] 0.2123501 1.958486 3.5675 2.095243 1.9262269 1.0693401 8.661433
#> [79,] 0.3335374 2.025497 3.6615 2.239480 1.7961307 1.0552698 9.222412
#> [80,] 0.3092397 2.065428 3.6000 2.142257 2.1771539 1.0411996 8.810848
#> [81,] 0.2295846 1.946362 3.5900 2.172486 1.9602265 1.0271293 9.041441
#> [82,] 0.3051289 1.750401 3.7165 2.212951 1.9861601 1.0130591 8.976698
#> [83,] 0.3766003 1.868461 3.7255 2.241732 1.2607942 0.9989888 9.155318
#> [84,] 0.3218062 2.244893 3.7255 2.207650 2.2289101 0.9849185 8.883817
#> [85,] 0.3315960 2.453008 3.7400 2.483217 2.3412281 0.9708483 9.471377
#> [86,] 0.3907655 2.338952 3.7720 2.200088 2.4630032 0.9567780 8.792609
#> [87,] 0.2239737 2.110105 3.8685 2.086612 2.3946244 0.9427077 8.507987
#> [88,] 0.3447672 1.872992 3.8300 2.200053 1.8566266 0.9286375 8.844567
#> [89,] 0.3512674 2.193702 3.8850 2.242377 2.1368718 0.9145672 9.185327
#> [90,] 0.5908428 2.120375 3.9000 2.336094 2.0172117 0.9004969 9.269376
#> [91,] 0.4942036 1.840511 3.9300 2.226913 1.6353091 0.8864267 9.094633
#> [92,] 0.2908909 1.875848 3.9400 2.246137 1.5206931 0.8723564 9.095980
#> [93,] 0.2921567 2.201174 3.9785 2.344417 1.8360493 0.8442159 9.165965
#> [94,] 0.4673250 1.948546 4.0520 2.069483 1.7821175 0.8160753 8.537248
#> [95,] 0.3101382 1.917943 4.0520 2.199439 1.3302648 0.8020051 8.834730
#> [96,] 0.3868214 2.395599 4.1140 2.271250 2.6094026 0.7879348 8.967005
#> [97,] 0.3452616 2.027365 4.1365 2.190545 1.9190915 0.7738646 8.727974
#> [98,] 0.3954911 2.039060 4.1500 2.186815 2.4460192 0.7597943 8.840677
#> [99,] 0.4073101 1.950669 4.1665 2.183462 1.4281282 0.7457240 8.767857
#> [100,] 0.3754839 2.328320 4.2585 2.488824 3.0881443 0.7175835 9.270213
#> [101,] 0.2517525 2.387514 4.2585 2.613092 2.6946755 0.6894430 9.322993
#> [102,] 0.3670538 2.872005 4.3465 2.713917 3.0326940 0.6753727 9.599115
#> [103,] 0.3298458 2.945118 4.3765 2.580394 3.7435067 0.6613024 9.411670
#> [104,] 0.4261636 2.583096 4.3800 2.343620 3.1708962 0.6472322 8.796464
#> [105,] 0.4892081 2.199106 4.3855 2.399867 2.0966110 0.6331619 8.794842
#> [106,] 0.4511112 2.264357 4.4200 2.314932 2.2958593 0.6190916 8.902869
#> [107,] 0.1917002 2.337725 4.4200 2.385651 2.7087961 0.6050214 8.709873
#> [108,] 0.2303994 2.691336 4.5100 2.734964 2.6902968 0.5909511 9.482888
#> [109,] 0.3632314 2.087051 4.6165 2.133163 2.4928663 0.5628106 8.287737
#> [110,] 0.1657329 2.991056 4.6700 2.505782 3.6266554 0.5487403 9.093049
#> [111,] 0.2555840 3.514591 4.6700 2.581461 4.9208384 0.5346701 9.371531
#> [112,] 0.1323844 3.023327 4.6920 2.615176 3.8370942 0.5205998 9.303265
#> [113,] 0.2785586 3.860122 4.6920 2.534569 5.5113924 0.5065295 9.478093
#> [114,] 0.1548645 3.186122 4.8500 2.906559 3.6203859 0.4783890 9.473590
#> [115,] 0.2103744 4.846319 4.8555 3.144348 6.9883587 0.4643187 10.213998
#> [116,] 0.1038590 3.703557 4.8555 2.932375 5.1329072 0.4502485 9.702158
#> [117,] 0.2144725 3.480823 5.1260 2.911565 5.1783066 0.4361782 9.452092
#> [,8] [,9] [,10] [,11]
#> [1,] 15.53757 20.05856 36.39741 47.05142
#> [2,] 15.50592 20.20227 37.55246 49.15112
#> [3,] 15.83069 20.21225 35.52685 45.25978
#> [4,] 19.99880 27.44142 57.66326 79.57431
#> [5,] 16.57381 21.55122 39.65129 51.56185
#> [6,] 17.67085 23.00705 42.34604 55.03145
#> [7,] 14.47039 18.12863 30.37702 37.85602
#> [8,] 15.67239 20.36564 37.48472 48.77622
#> [9,] 13.96311 17.46895 29.60467 37.10935
#> [10,] 15.09317 19.48950 35.52522 46.15040
#> [11,] 13.96444 18.01109 32.68725 42.31824
#> [12,] 16.66178 21.49864 38.78635 50.00097
#> [13,] 14.89954 19.38677 35.90720 46.89450
#> [14,] 17.74985 23.61242 46.00526 61.39427
#> [15,] 17.25544 22.55126 41.96479 54.82812
#> [16,] 19.09112 26.09474 54.52123 75.15318
#> [17,] 14.82754 18.52116 31.27038 39.10277
#> [18,] 17.98558 23.46299 44.06584 57.80574
#> [19,] 15.57134 20.29116 37.68581 49.27841
#> [20,] 17.04954 22.33813 42.10981 56.18439
#> [21,] 16.03304 20.97473 39.39906 51.79658
#> [22,] 14.28099 17.50843 28.50376 35.06004
#> [23,] 16.63908 21.49314 38.83846 50.07651
#> [24,] 16.26041 21.35567 41.36946 55.35522
#> [25,] 16.11524 20.98250 38.76907 50.51958
#> [26,] 18.83561 25.39966 51.30302 69.66769
#> [27,] 16.81120 21.98112 40.98769 53.61176
#> [28,] 15.40189 19.55460 35.52383 46.05774
#> [29,] 17.07205 22.17172 40.58855 52.62864
#> [30,] 20.87561 29.19702 64.49043 91.07725
#> [31,] 14.07515 17.45357 29.02226 36.05938
#> [32,] 15.57948 19.65858 33.83614 42.79339
#> [33,] 15.41892 20.29294 38.73603 51.30574
#> [34,] 16.21878 21.83306 44.39038 60.65870
#> [35,] 14.86797 19.01472 34.91955 45.75726
#> [36,] 16.50337 21.15640 37.47283 47.86621
#> [37,] 16.52889 22.11717 43.97482 59.32702
#> [38,] 18.48780 25.60162 55.59620 78.10893
#> [39,] 16.13788 21.31510 40.97593 54.41677
#> [40,] 14.85199 18.64644 31.80129 40.11633
#> [41,] 14.49149 18.45339 32.33735 41.17468
#> [42,] 13.71730 17.11013 28.91111 36.25260
#> [43,] 15.78084 20.85105 42.06553 57.25186
#> [44,] 17.50249 22.90917 42.72991 55.86322
#> [45,] 14.38986 18.19551 31.71170 40.26925
#> [46,] 15.02650 19.20342 33.93144 43.37795
#> [47,] 16.38244 21.22019 38.61871 49.95359
#> [48,] 15.32911 19.49891 34.71000 44.73763
#> [49,] 16.88468 22.24651 42.36695 55.98933
#> [50,] 14.71009 18.97870 34.79513 45.31106
#> [51,] 14.69908 18.41665 30.80710 38.34200
#> [52,] 14.87930 19.00015 33.46826 42.77044
#> [53,] 15.39067 19.90494 37.85568 50.40779
#> [54,] 15.48264 20.01877 36.49526 47.35057
#> [55,] 16.98734 22.68680 44.82617 60.27849
#> [56,] 16.09376 20.65937 36.87546 47.39964
#> [57,] 15.26979 20.12341 38.77008 51.69949
#> [58,] 14.01545 16.87127 25.43341 30.23372
#> [59,] 14.15767 18.14761 32.42174 41.67882
#> [60,] 19.25995 26.98888 61.60228 88.92639
#> [61,] 16.19980 20.20915 34.85690 44.03001
#> [62,] 14.66543 18.57095 32.67045 41.98167
#> [63,] 14.20864 18.26295 32.87186 42.40836
#> [64,] 16.20322 21.17623 39.48663 51.66539
#> [65,] 16.01611 20.80028 38.21978 51.01364
#> [66,] 14.96509 19.34531 35.39830 45.98087
#> [67,] 13.93658 17.23326 29.63091 37.42716
#> [68,] 14.92874 18.65448 31.29704 38.98927
#> [69,] 14.72341 18.56668 33.41585 43.32225
#> [70,] 12.90615 15.64717 25.06891 30.63968
#> [71,] 15.43271 19.39310 32.62194 40.76677
#> [72,] 14.06618 17.07038 26.18930 31.27654
#> [73,] 14.36033 17.84286 29.20191 35.97684
#> [74,] 14.94452 18.97239 33.88387 44.12519
#> [75,] 13.71983 16.58635 25.42349 30.77785
#> [76,] 16.13319 20.58404 35.90848 45.50590
#> [77,] 13.79631 16.55734 24.66431 29.15465
#> [78,] 13.56489 16.28303 24.38171 28.85147
#> [79,] 15.46217 19.23738 33.52331 42.63513
#> [80,] 15.01350 18.90539 31.95051 39.92577
#> [81,] 14.47499 17.37602 25.78962 30.29074
#> [82,] 15.64454 19.76379 33.63137 42.15488
#> [83,] 14.94852 18.69653 33.71160 43.76291
#> [84,] 14.41930 17.88323 31.05870 39.51083
#> [85,] 13.88403 16.66875 28.11069 35.34433
#> [86,] 14.18316 18.23727 33.46594 43.61164
#> [87,] 12.84999 15.25506 22.88416 27.20098
#> [88,] 15.43401 19.46932 33.48184 42.24607
#> [89,] 15.96503 20.33707 35.42199 44.89007
#> [90,] 17.73180 25.10412 59.48407 88.46561
#> [91,] 18.56081 25.73326 56.25050 79.32676
#> [92,] 15.04239 18.41685 28.95915 34.97434
#> [93,] 14.18332 17.03313 26.98950 33.21589
#> [94,] 15.28644 20.11201 39.13805 52.49441
#> [95,] 14.22361 17.70648 29.19627 36.13384
#> [96,] 14.79216 18.80519 33.26946 43.16925
#> [97,] 14.72355 18.37194 30.39274 38.07560
#> [98,] 15.12801 19.08741 35.19091 46.07193
#> [99,] 15.84979 20.80500 39.47857 52.15707
#> [100,] 15.91963 20.32617 36.23994 47.13405
#> [101,] 14.50979 17.05149 26.03958 31.38496
#> [102,] 13.81539 15.98053 23.68559 29.95030
#> [103,] 15.88308 20.23861 35.43654 45.12910
#> [104,] 16.05169 21.22164 41.17729 55.02351
#> [105,] 15.74155 20.99916 44.48038 62.19405
#> [106,] 15.98210 21.32069 43.36119 59.56973
#> [107,] 13.77874 16.56847 24.71764 29.10899
#> [108,] 14.64995 17.51478 26.19356 31.35739
#> [109,] 13.11528 16.04241 27.58557 34.98283
#> [110,] 12.89622 14.84978 19.79069 22.54095
#> [111,] 12.97283 14.71246 22.78152 27.47686
#> [112,] 13.93753 16.06769 21.24508 23.57985
#> [113,] 15.04068 18.96591 33.12331 42.62357
#> [114,] 14.37786 16.64387 22.38575 25.20496
#> [115,] 13.87039 16.23303 24.71913 29.85160
#> [116,] 13.77463 15.70458 21.54072 24.62706
#> [117,] 14.90087 18.10407 27.54314 32.67455
#>
#> $CI_Lower
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 0.145364427 0.7807680 2.38 1.103980 -0.0661689322 3.2361609 7.087070
#> [2,] 0.166978743 0.8164501 2.39 1.143581 -0.0833317579 3.2080203 6.948133
#> [3,] 0.180813719 0.8281051 2.40 1.095241 0.1052161728 3.1798798 6.943937
#> [4,] 0.194180269 0.8427989 2.41 1.184696 -0.2710925448 3.1235988 7.187779
#> [5,] 0.199659144 0.7501491 2.42 1.085966 -0.1066947328 3.1095285 6.858255
#> [6,] 0.195406099 0.8241344 2.43 1.168328 -0.0832117092 3.0673177 7.352245
#> [7,] 0.177219842 0.9025287 2.44 1.160208 0.1622991713 3.0391772 6.976059
#> [8,] 0.197636196 0.8743004 2.45 1.176768 -0.0577567567 2.9969664 7.370785
#> [9,] 0.114663591 0.9188449 2.46 1.250828 0.1334703531 2.9406853 7.298994
#> [10,] 0.178051746 0.8423615 2.47 1.143772 0.0135473394 2.8984745 6.981219
#> [11,] 0.129679073 0.7867049 2.48 1.234824 -0.1464757642 2.8844043 7.544493
#> [12,] 0.172148585 0.8978799 2.49 1.156311 0.0825455323 2.8703340 6.981420
#> [13,] 0.157604363 0.8247315 2.50 1.179272 -0.1511804926 2.8140529 7.184605
#> [14,] 0.270316641 0.8323795 2.52 1.194698 -0.1312531293 2.7999827 7.372274
#> [15,] 0.119118414 0.9140639 2.53 1.080429 0.0002799355 2.7859124 6.639062
#> [16,] 0.201373459 0.7334024 2.54 1.109985 -0.2636343280 2.7296313 7.091664
#> [17,] 0.162989728 0.8580673 2.55 1.219929 -0.0135151510 2.6874205 7.432000
#> [18,] 0.131212541 0.8471416 2.56 1.178963 -0.0405853585 2.6311395 7.184870
#> [19,] 0.035217138 0.8566145 2.57 1.277186 -0.1420829652 2.6029990 7.134340
#> [20,] 0.182465152 0.8538834 2.58 1.315522 -0.2293736530 2.5748584 7.489172
#> [21,] 0.142319790 0.8565102 2.60 1.224177 -0.1962957879 2.5467179 7.107127
#> [22,] 0.183521196 0.9301676 2.61 1.219659 0.2117177500 2.5185774 7.159847
#> [23,] 0.183301719 0.9335466 2.62 1.190494 0.0606540923 2.5045071 6.992069
#> [24,] 0.172450099 0.7353175 2.63 1.092420 -0.2978946654 2.4763666 6.993532
#> [25,] 0.179171950 0.9314842 2.64 1.243799 -0.0387227027 2.4482260 7.245934
#> [26,] 0.202113150 0.8862557 2.65 1.202029 -0.2656176223 2.4200855 6.998980
#> [27,] 0.140299129 0.8410596 2.66 1.249365 -0.2411615003 2.4060153 7.097437
#> [28,] 0.151211023 0.8898171 2.67 1.256456 -0.0642437213 2.3778747 7.358779
#> [29,] 0.157250624 0.9092916 2.69 1.273607 -0.0450214644 2.3638045 7.156532
#> [30,] 0.185108025 0.7677410 2.70 1.233473 -0.5241590877 2.3497342 7.236461
#> [31,] 0.180453489 0.9224474 2.72 1.216476 0.1242511292 2.3215937 7.298749
#> [32,] 0.179813554 0.8382030 2.73 1.169198 -0.0493389116 2.2793829 7.053251
#> [33,] 0.177866951 0.8560246 2.75 1.234712 -0.2775663934 2.2512423 7.399147
#> [34,] 0.152614455 0.8049968 2.76 1.236687 -0.4441707542 2.1808910 7.036630
#> [35,] 0.088791780 0.8446472 2.78 1.247899 -0.2562837591 2.1527505 7.004003
#> [36,] 0.151694645 0.9384223 2.80 1.235786 -0.1089048264 2.1386802 7.105157
#> [37,] 0.124858715 0.8838574 2.82 1.251470 -0.3453034120 2.0964694 6.964749
#> [38,] 0.193062087 0.8349928 2.84 1.242187 -0.5578288790 2.0683289 7.191655
#> [39,] 0.135556135 0.8956292 2.85 1.224356 -0.2313492589 2.0542586 6.888643
#> [40,] 0.094325051 0.8332295 2.86 1.110385 0.0016715467 2.0120478 6.837924
#> [41,] 0.148654721 0.8314902 2.87 1.257961 -0.2302065502 1.9698371 7.318232
#> [42,] 0.139244377 0.9364172 2.88 1.142331 0.0910935806 1.9557668 6.635011
#> [43,] 0.083167528 0.8454134 2.89 1.333412 -0.4390337076 1.9276263 7.612224
#> [44,] 0.114515530 1.0151346 2.90 1.299216 0.0006347623 1.8854155 7.153166
#> [45,] 0.077370467 0.9511479 2.91 1.236362 0.0139912052 1.8291344 6.904270
#> [46,] 0.047656221 1.0761420 2.92 1.371093 0.1163690672 1.8150641 7.272833
#> [47,] 0.166583179 1.0735856 2.94 1.346441 0.0806354307 1.8009939 7.246063
#> [48,] 0.158122286 1.0294266 2.95 1.379266 -0.0066934070 1.7728533 7.337252
#> [49,] 0.087300823 1.0632463 2.97 1.421613 -0.0730105232 1.7447128 7.313480
#> [50,] 0.083646797 0.9434821 3.00 1.329329 -0.1631951423 1.7306426 7.167723
#> [51,] 0.132366569 1.0993112 3.02 1.325343 0.2181183005 1.7025020 7.099095
#> [52,] 0.096922510 0.9860102 3.04 1.395408 -0.0768779989 1.6743615 7.424656
#> [53,] 0.136467775 0.9020870 3.05 1.316212 -0.3814017394 1.6602912 7.125000
#> [54,] 0.145949241 0.9630585 3.06 1.260692 -0.0839437371 1.6462210 6.940078
#> [55,] 0.157254091 1.0043304 3.07 1.346664 -0.2542142234 1.6321507 7.253427
#> [56,] -0.016147633 1.0693173 3.08 1.399437 0.0135601796 1.5758696 7.220151
#> [57,] 0.046678892 0.9208956 3.09 1.368644 -0.3797754691 1.5617994 7.106458
#> [58,] 0.118666781 1.0319898 3.12 1.298964 0.1980918403 1.5477291 7.044970
#> [59,] 0.040963041 1.0396028 3.13 1.340142 -0.0970746726 1.5336588 6.929676
#> [60,] 0.018011005 1.0083081 3.14 1.415925 -0.5716493952 1.5055183 7.061197
#> [61,] 0.096415889 1.0917239 3.15 1.440637 0.2164898111 1.4914481 7.474270
#> [62,] 0.109748319 1.0568865 3.16 1.314452 0.0054206924 1.4773778 6.996242
#> [63,] -0.025588352 0.9767252 3.17 1.328476 -0.1543289629 1.4492373 6.898784
#> [64,] 0.075556066 1.1348773 3.19 1.280510 -0.0483788187 1.4210967 6.767256
#> [65,] 0.006091468 0.8804454 3.20 1.259760 -0.4671844646 1.4070265 6.829730
#> [66,] -0.058416588 1.0365780 3.22 1.392379 -0.1399314523 1.3929562 6.959900
#> [67,] 0.104592273 1.0763389 3.23 1.433913 0.0201597129 1.3788859 7.378316
#> [68,] 0.057657592 1.1328104 3.25 1.320521 0.3000122328 1.3648157 6.987234
#> [69,] -0.070612509 1.0507312 3.28 1.404053 -0.1534977138 1.3226049 7.311570
#> [70,] 0.009796503 1.1153609 3.30 1.495940 0.2023354661 1.2944643 7.302792
#> [71,] 0.128551174 1.1432649 3.31 1.464846 0.1273971186 1.2803941 7.250941
#> [72,] -0.191993999 1.2375612 3.35 1.184433 0.6349147317 1.2663238 6.455012
#> [73,] -0.037291422 1.0477923 3.37 1.382678 0.1379800675 1.2241130 7.073396
#> [74,] 0.020440382 1.1257317 3.41 1.483326 -0.1194010414 1.2100428 7.263981
#> [75,] 0.023181491 1.2634936 3.42 1.535196 0.4095642412 1.1819022 7.544566
#> [76,] -0.095989469 1.2942489 3.45 1.453476 0.3147577487 1.1537617 7.148863
#> [77,] -0.049748014 1.3708129 3.48 1.636423 0.5579625282 1.0974806 7.505704
#> [78,] -0.072385053 1.3985818 3.49 1.364533 0.7554138680 1.0693401 6.796487
#> [79,] 0.037622834 1.1612383 3.54 1.469333 0.1057326324 1.0552698 7.178612
#> [80,] -0.044039183 1.3450163 3.57 1.652378 0.3545414350 1.0411996 7.615237
#> [81,] -0.021238284 1.2306195 3.59 1.485315 0.5221080204 1.0271293 7.162373
#> [82,] -0.066098503 1.3879043 3.60 1.534382 0.4742273190 1.0130591 7.196894
#> [83,] 0.061917260 1.1938264 3.63 1.469556 -0.1799065800 0.9989888 7.123658
#> [84,] -0.025802866 1.2684809 3.70 1.391486 0.1332267548 0.9849185 7.051459
#> [85,] 0.020547314 1.1637562 3.72 1.478203 -0.0435545276 0.9708483 7.197562
#> [86,] -0.033541568 1.1289359 3.73 1.449963 -0.3432944546 0.9567780 7.115863
#> [87,] -0.076074658 1.1269820 3.74 1.272351 0.3946981470 0.9427077 6.718516
#> [88,] -0.006698013 1.2637668 3.75 1.471189 0.0400043104 0.9286375 7.254924
#> [89,] 0.014994801 1.2297047 3.79 1.409831 -0.0289427359 0.9145672 7.009473
#> [90,] -0.004575039 0.8381407 3.83 1.375992 -1.4434857437 0.9004969 7.035936
#> [91,] 0.028907965 1.0078718 3.90 1.422794 -0.6401557835 0.8864267 7.190805
#> [92,] 0.040289178 1.1568388 3.93 1.341387 0.1291004248 0.8723564 7.149888
#> [93,] 0.081035868 1.3312140 3.94 1.637717 0.2279347000 0.8442159 7.592926
#> [94,] 0.039443824 0.8459192 4.01 1.234612 -0.9687228534 0.8160753 6.571981
#> [95,] 0.146188556 1.1241377 4.02 1.382474 0.0599894682 0.8020051 6.968772
#> [96,] -0.057202325 1.1056991 4.03 1.550723 -0.4275113618 0.7879348 7.281201
#> [97,] 0.026602768 1.0936990 4.07 1.453618 -0.1067873346 0.7738646 7.112590
#> [98,] -0.120134295 1.2433298 4.12 1.446157 -0.3394709679 0.7597943 7.207642
#> [99,] 0.091412115 1.1781580 4.15 1.380292 -0.2836604034 0.7457240 7.078274
#> [100,] -0.251265239 1.3733635 4.18 1.404510 -0.2166725450 0.7175835 6.980932
#> [101,] -0.153350786 1.3746297 4.20 1.546480 0.3172690189 0.6894430 7.285144
#> [102,] -0.065410761 0.9497640 4.22 1.395646 -0.6158603093 0.6753727 6.884611
#> [103,] -0.191510544 1.3680512 4.29 1.678160 -0.0267903080 0.6613024 7.452393
#> [104,] -0.149100240 1.3497762 4.33 1.467370 -0.3919370624 0.6472322 7.196434
#> [105,] -0.015980478 1.1359808 4.36 1.401100 -0.9120074109 0.6331619 6.926052
#> [106,] -0.007537024 1.1015866 4.38 1.343000 -0.5613824043 0.6190916 6.839523
#> [107,] -0.123251777 1.4054343 4.39 1.499884 0.8216314912 0.6050214 7.190480
#> [108,] -0.074496045 1.2561563 4.42 1.195381 0.8181069941 0.5909511 6.707018
#> [109,] -0.113579091 1.0838857 4.51 1.516463 -0.4210981002 0.5628106 7.049787
#> [110,] -0.198870254 1.4195469 4.54 1.425897 0.7222226452 0.5487403 7.070900
#> [111,] -0.325250453 1.3136232 4.60 1.556618 0.2820147026 0.5346701 7.244170
#> [112,] -0.194370632 1.5083983 4.63 1.568446 0.9408832726 0.5205998 7.301234
#> [113,] -0.353591059 1.7803065 4.67 1.831014 0.5744703465 0.5065295 7.857607
#> [114,] -0.128344063 1.5291214 4.71 1.565044 0.9844789624 0.4783890 7.192134
#> [115,] -0.452748531 1.6592302 4.74 1.638545 0.7679220996 0.4643187 7.422998
#> [116,] -0.359349610 1.9285864 4.85 1.657094 1.4856707185 0.4502485 7.596711
#> [117,] -0.419708039 2.0279592 4.86 1.945113 1.1384415966 0.4361782 7.980334
#> [,8] [,9] [,10] [,11]
#> [1,] 10.280848 11.925818 16.581453 19.028970
#> [2,] 10.152725 11.824397 16.549863 19.015358
#> [3,] 10.577816 12.598557 18.030483 20.873711
#> [4,] 10.779941 12.709975 18.340652 21.368140
#> [5,] 10.349995 12.275501 18.076426 21.300855
#> [6,] 11.122411 13.155720 19.134401 22.375747
#> [7,] 10.284683 12.031306 17.033391 19.676548
#> [8,] 11.224193 13.333587 19.640293 23.120269
#> [9,] 10.718669 12.395493 16.806281 18.995536
#> [10,] 10.562215 12.473762 18.064267 21.049906
#> [11,] 10.905263 12.588444 17.118471 19.385618
#> [12,] 10.337561 12.133193 17.369225 20.153401
#> [13,] 10.971621 12.946775 18.100618 20.764360
#> [14,] 12.069564 14.741279 23.267323 28.249648
#> [15,] 9.652217 11.237006 15.079294 16.951880
#> [16,] 11.080612 13.197437 19.439267 22.869948
#> [17,] 11.224215 13.198291 18.625064 21.436242
#> [18,] 10.559208 12.172293 16.540554 18.728476
#> [19,] 9.592338 10.696002 13.369486 14.570809
#> [20,] 11.375450 13.484652 19.444698 22.615122
#> [21,] 10.580247 12.381222 17.201899 19.605329
#> [22,] 10.907705 12.883341 18.637724 21.717946
#> [23,] 10.385433 12.195015 17.436129 20.236373
#> [24,] 10.783756 12.629484 17.885919 20.647670
#> [25,] 10.903467 12.797918 18.226485 21.095451
#> [26,] 10.567811 12.515771 18.295595 21.446243
#> [27,] 10.261250 11.877858 16.365306 18.672264
#> [28,] 10.803815 12.561127 17.405927 19.887952
#> [29,] 10.550041 12.344401 17.526167 20.298682
#> [30,] 10.940730 12.863374 18.404743 21.349324
#> [31,] 11.247867 13.275000 19.228828 22.464047
#> [32,] 11.169192 13.526606 19.864628 23.042035
#> [33,] 11.849991 14.203292 20.559068 23.845066
#> [34,] 10.216871 11.848251 16.379084 18.703533
#> [35,] 9.971941 11.383235 15.164122 17.050001
#> [36,] 10.455846 12.210806 17.243031 19.867298
#> [37,] 9.956122 11.471067 15.645272 17.778839
#> [38,] 11.156069 13.390834 20.080272 23.602729
#> [39,] 9.851206 11.355779 15.505807 17.626497
#> [40,] 10.090402 11.780069 15.805882 17.653579
#> [41,] 11.707512 13.707217 19.336802 22.249862
#> [42,] 9.688171 11.303856 15.940682 18.394878
#> [43,] 10.739464 12.236610 16.129445 18.011223
#> [44,] 10.470074 12.027136 16.183950 18.238428
#> [45,] 10.265087 11.845464 15.671093 17.386661
#> [46,] 10.450014 11.923547 15.200692 16.694560
#> [47,] 10.844944 12.684004 17.883507 20.601259
#> [48,] 11.317915 13.238478 18.605430 21.379650
#> [49,] 10.276074 11.687621 15.319115 17.049866
#> [50,] 10.310750 11.735249 15.418855 17.185206
#> [51,] 10.220866 11.798982 16.127478 18.326247
#> [52,] 11.277323 13.126824 17.844746 20.188737
#> [53,] 10.669962 12.353510 16.948683 19.270205
#> [54,] 10.509790 12.460985 18.158704 20.750655
#> [55,] 10.787247 12.574125 17.576331 20.163749
#> [56,] 9.574501 10.566992 12.832656 13.792023
#> [57,] 9.796747 11.053418 14.240758 15.745488
#> [58,] 10.638832 12.426309 16.820059 18.993177
#> [59,] 9.616513 10.894700 13.999302 15.331150
#> [60,] 9.484221 10.550463 13.080282 14.193568
#> [61,] 10.932570 12.647440 17.342398 19.611801
#> [62,] 9.977639 11.459508 15.449855 17.391892
#> [63,] 9.574514 10.550094 12.753772 13.677056
#> [64,] 9.559601 10.941892 14.642841 16.476697
#> [65,] 9.195253 10.188553 12.505377 13.509589
#> [66,] 8.993361 9.826960 11.685215 12.458157
#> [67,] 11.397161 13.263648 17.944986 20.251437
#> [68,] 9.697234 10.941786 14.059777 15.484125
#> [69,] 9.820365 10.756356 12.813225 13.655588
#> [70,] 9.932078 11.062621 13.718906 14.874362
#> [71,] 10.884275 12.648484 17.275559 19.583207
#> [72,] 7.764126 8.216590 9.065942 9.360123
#> [73,] 9.907555 11.054804 13.611346 14.654363
#> [74,] 9.863585 11.009721 13.738181 14.943294
#> [75,] 10.983973 12.379620 15.667945 17.138307
#> [76,] 9.248035 10.093502 11.954409 12.721003
#> [77,] 10.091250 11.177069 13.464673 14.404953
#> [78,] 9.020432 9.991022 11.963821 12.707076
#> [79,] 10.765809 12.397325 16.188245 17.873866
#> [80,] 10.877748 12.035374 14.596719 15.648282
#> [81,] 10.116778 11.366966 13.927021 15.014809
#> [82,] 9.619046 10.682278 13.236117 14.280463
#> [83,] 10.023651 11.365192 14.804343 16.444235
#> [84,] 9.527430 10.623648 13.263993 14.447599
#> [85,] 10.651926 12.420720 16.953764 19.129458
#> [86,] 10.367936 12.041736 15.054827 16.361373
#> [87,] 9.463293 10.808988 13.555424 14.743712
#> [88,] 10.260407 11.472994 14.394171 15.710244
#> [89,] 9.833870 11.200975 14.689628 16.018293
#> [90,] 10.519404 11.756914 14.594449 15.819119
#> [91,] 10.707513 12.057692 15.402765 16.953580
#> [92,] 10.122828 11.553193 15.137953 16.829604
#> [93,] 11.247655 12.977365 17.400010 19.536079
#> [94,] 10.161729 11.638329 15.510968 17.440848
#> [95,] 10.368736 12.254305 17.653041 20.194132
#> [96,] 11.191032 12.804671 16.393767 17.741459
#> [97,] 10.506631 12.058189 16.078030 18.081317
#> [98,] 9.576935 10.577354 12.430392 13.067681
#> [99,] 9.980042 11.405616 15.137126 16.862120
#> [100,] 9.002973 9.908703 12.211845 12.957235
#> [101,] 9.467531 10.196779 11.619631 12.132456
#> [102,] 10.397379 12.211105 15.319964 16.670732
#> [103,] 10.900514 12.014086 13.837986 14.490502
#> [104,] 10.063164 11.393788 13.665265 14.467913
#> [105,] 9.789569 10.878510 13.426140 14.534674
#> [106,] 9.665998 11.119867 15.160845 16.829697
#> [107,] 10.086623 11.213885 13.282136 14.009368
#> [108,] 8.809952 9.672202 11.496449 12.163244
#> [109,] 9.959690 10.887267 12.738540 13.433245
#> [110,] 9.306745 10.069166 11.608992 12.185787
#> [111,] 10.428975 11.592068 13.436024 13.798269
#> [112,] 9.768111 10.799095 12.827781 13.400680
#> [113,] 10.943249 12.108510 13.754065 14.355490
#> [114,] 9.951536 11.245225 13.684530 14.432939
#> [115,] 10.178379 11.364617 13.341227 13.898571
#> [116,] 9.471763 10.011160 10.922780 11.210548
#> [117,] 10.128101 10.670233 11.501490 11.734216
#>
#> $AR2
#> [1] 0.07595597 0.07687889 0.10877922 0.06874862 0.09253276 0.07995122
#> [7] 0.09450850 0.11554879 0.10275522 0.07660460 0.07479189 0.12175506
#> [13] 0.07776721 0.07871171 0.12418588 0.10410928 0.12892200 0.09718445
#> [19] 0.09927318 0.10065842 0.09626834 0.08458467 0.09691104 0.09831975
#> [25] 0.09979986 0.08774191 0.10104084 0.08901669 0.09297834 0.10687950
#> [31] 0.13083332 0.10935766 0.18177721 0.10349987 0.09770173 0.13695849
#> [37] 0.12485298 0.13417545 0.15678986 0.13833079 0.10118107 0.11247252
#> [43] 0.12184699 0.13755279 0.07259651 0.07325172 0.09018448 0.08943510
#> [49] 0.07698744 0.10240940 0.10469934 0.09840832 0.09977064 0.10102947
#> [55] 0.15251127 0.07347544 0.07352994 0.08989795 0.09923084 0.07866187
#> [61] 0.07810503 0.08959925 0.08438595 0.06895969 0.06871350 0.07183221
#> [67] 0.07115286 0.11381371 0.08786905 0.07070965 0.07070952 0.12088132
#> [73] 0.07273948 0.09741227 0.09316958 0.17055570 0.11040104 0.10278976
#> [79] 0.08811505 0.08555441 0.08710663 0.09327651 0.09117414 0.08055814
#> [85] 0.08162753 0.08359350 0.08681969 0.09165906 0.08864231 0.08814073
#> [91] 0.09795251 0.12551786 0.11860210 0.10172109 0.09699049 0.09364459
#> [97] 0.09901705 0.11256242 0.13822240 0.12843157 0.09062362 0.08980702
#> [103] 0.10118658 0.10565831 0.10487678 0.09921103 0.09196793 0.12792166
#> [109] 0.09584450 0.09517302 0.09977096 0.09841095 0.14288080 0.10549838
#> [115] 0.11414374 0.11088276 0.12464015
#>
#> $AR2_pValue
#> [1] 0.08914088 0.09369123 0.29700173 0.05579041 0.18683768 0.11040807
#> [7] 0.20024202 0.34247064 0.25680171 0.09249332 0.08348755 0.38424786
#> [13] 0.09823620 0.10331959 0.39953202 0.26601111 0.42935724 0.21946982
#> [19] 0.23382847 0.24347008 0.21341326 0.13787533 0.21756396 0.22721078
#> [25] 0.23755999 0.15741081 0.24581077 0.16575510 0.19138591 0.28594165
#> [31] 0.44225404 0.30324518 0.69133394 0.26370243 0.22366936 0.48078539
#> [37] 0.40614179 0.46266888 0.58586855 0.48898398 0.24819777 0.32589512
#> [43] 0.38816819 0.48725737 0.07380321 0.07711099 0.17503682 0.16937813
#> [49] 0.09594814 0.25763752 0.27378093 0.22998901 0.23969711 0.24806620
#> [55] 0.56967307 0.07825805 0.07826956 0.17282192 0.23640110 0.10554051
#> [61] 0.10224323 0.17195162 0.13915996 0.05782713 0.05658216 0.07037672
#> [67] 0.06762536 0.33914068 0.16186181 0.06557926 0.06562820 0.38868040
#> [73] 0.07479090 0.22620251 0.19751656 0.66116547 0.31949185 0.26629071
#> [79] 0.16452221 0.14852871 0.15831299 0.19940428 0.18588440 0.11809958
#> [85] 0.12419053 0.13591440 0.15702841 0.18990033 0.16903105 0.16574717
#> [91] 0.23314270 0.42386503 0.37887627 0.26004999 0.22728611 0.20364899
#> [97] 0.24161050 0.33730818 0.50473682 0.44443819 0.18357196 0.17818814
#> [103] 0.25906103 0.29167249 0.28645171 0.24551758 0.19369650 0.44781691
#> [109] 0.22090005 0.21635056 0.25018536 0.23977410 0.54314403 0.29255598
#> [115] 0.35729070 0.33338069 0.43389524
#>
#> $Candidate_Thres
#> [1] 2.4
#>