TH: Sequential Goodness of Fit Testing for the Generalized Pareto...
In tea: Threshold Estimation Approaches
Description
Usage
Arguments
Details
Value
References
Examples
Description
An implementation of the sequential testing procedure proposed in Thompson et al. (2009) for automated threshold selection
Usage
1
Arguments
data
vector of sample data
thresholds
a sequence of pre-defined thresholds to check for GPD assumption
Details
The procedure proposed in Thompson et al. (2009) is based on sequential goodness of fit testing. First, one has to choose a equally spaced grid of posssible thresholds. The authors recommend 100 thresholds between the 50 percent and 98 percent quantile of the data, provided there are enough observations left (about 100 observations above the last pre-defined threshold). Then the parameters of a GPD for each threshold are estimated. One can show that the differences of subsequent scale parameters are approximately normal distributed. So a Pearson chi-squared test for normality is applied to all the differences, striking the smallest thresholds out until the test is not rejected anymore.
Value
threshold
the threshold used for the test
num.above
the number of observations above the given threshold
p.values
raw p-values for the thresholds tested
ForwardStop
transformed p-values according to the ForwardStop criterion. See G'Sell et al (2016) for more information
StrongStop
transformed p-values according to the StrongStop criterion. See G'Sell et al (2016) for more information
est.scale
estimated scale parameter for the given threshold
est.shape
estimated shape parameter for the given threshold
References
Thompson, P. and Cai, Y. and Reeve, D. (2009). Automated threshold selection methods for extreme wave analysis. Coastal Engineering, 56(10), 1013–1021.
G'Sell, M.G. and Wager, S. and Chouldechova, A. and Tibshirani, R. (2016). Sequential selection procedures and false discovery rate control. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 78(2), 423–444.
Examples
1
2
3
Example output
Loading required package: eva
testnum threshold num.above p.values ForwardStop StrongStop
[1,] 1 0.1069378 900 0.020061467 0.02026543 0.0001224283
[2,] 2 0.1284360 881 0.043764781 0.03250839 0.0030513307
[3,] 3 0.1499341 861 0.073231143 0.04702262 0.0097237915
[4,] 4 0.1714323 832 0.032786177 0.04360089 0.0174313744
[5,] 5 0.1929305 817 0.047948401 0.04470792 0.0327716963
[6,] 6 0.2144287 798 0.042195689 0.04444190 0.0501375202
[7,] 7 0.2359269 781 0.068181693 0.04818126 0.0728346516
[8,] 8 0.2574250 761 0.039442099 0.04718873 0.0935330268
[9,] 9 0.2789232 747 0.059978784 0.04881808 0.1245424668
[10,] 10 0.3004214 739 0.083696948 0.05267708 0.1532279569
[11,] 11 0.3219196 719 0.037366046 0.05135026 0.1785148559
[12,] 12 0.3434177 702 0.057975184 0.05204804 0.2206279896
[13,] 13 0.3649159 691 0.100853782 0.05622201 0.2582032218
[14,] 14 0.3864141 678 0.064024295 0.05693228 0.2860329308
[15,] 15 0.4079123 666 0.104700023 0.06050989 0.3248732089
[16,] 16 0.4294105 652 0.122325228 0.06488297 0.3540153196
[17,] 17 0.4509086 640 0.143942088 0.07020852 0.3799473022
[18,] 18 0.4724068 626 0.133124057 0.07424468 0.4021778483
[19,] 19 0.4939050 616 0.187505819 0.08126583 0.4261764668
[20,] 20 0.5154032 600 0.191686741 0.08784281 0.4421559274
[21,] 21 0.5369013 589 0.250574371 0.09739545 0.4573582828
[22,] 22 0.5583995 576 0.281018518 0.10796473 0.4663105346
[23,] 23 0.5798977 563 0.293933848 0.11840307 0.4725280288
[24,] 24 0.6013959 555 0.598819809 0.15152563 0.4775993768
[25,] 25 0.6228941 547 0.498313073 0.17305576 0.4683972226
[26,] 26 0.6443922 536 0.628677920 0.20450306 0.4631065043
[27,] 27 0.6658904 524 0.699593947 0.24147036 0.4539868001
[28,] 28 0.6873886 504 0.706148713 0.27658504 0.4436039467
[29,] 29 0.7088868 490 0.681017434 0.30644828 0.4336626308
[30,] 30 0.7303849 484 0.439071869 0.31550542 0.4247974565
[31,] 31 0.7518831 471 0.465218545 0.32551805 0.4225294148
[32,] 32 0.7733813 460 0.530299574 0.33895999 0.4195554869
[33,] 33 0.7948795 452 0.567515095 0.35408872 0.4149866765
[34,] 34 0.8163777 448 0.501132281 0.36412771 0.4097551363
[35,] 35 0.8378758 440 0.473484843 0.37205192 0.4062189778
[36,] 36 0.8593740 433 0.556991203 0.38433286 0.4034620786
[37,] 37 0.8808722 424 0.611718139 0.39951369 0.3989911537
[38,] 38 0.9023704 415 0.750658833 0.42555105 0.3936862769
[39,] 39 0.9238685 400 0.738140064 0.44899706 0.3864978589
[40,] 40 0.9453667 387 0.606231873 0.46107196 0.3797805901
[41,] 41 0.9668649 378 0.681362473 0.47772145 0.3751828088
[42,] 42 0.9883631 369 0.471370725 0.48152494 0.3696931834
[43,] 43 1.0098613 357 0.358836516 0.48066321 0.3676201928
[44,] 44 1.0313594 352 0.595371752 0.49030238 0.3679309982
[45,] 45 1.0528576 345 0.682140151 0.50487665 0.3640197867
[46,] 46 1.0743558 335 0.583597610 0.51294680 0.3591462784
[47,] 47 1.0958540 324 0.490086522 0.51636312 0.3556442842
[48,] 48 1.1173521 316 0.487005024 0.51951158 0.3535594056
[49,] 49 1.1388503 308 0.445393229 0.52093984 0.3515744228
[50,] 50 1.1603485 302 0.298646343 0.51761590 0.3502771809
[51,] 51 1.1818467 295 0.270720238 0.51365672 0.3518102837
[52,] 52 1.2033449 287 0.057437734 0.50491627 0.3539993032
[53,] 53 1.2248430 282 0.037105950 0.49610298 0.3669369710
[54,] 54 1.2463412 280 0.237422850 0.49193536 0.3832350415
[55,] 55 1.2678394 274 0.286158526 0.48912007 0.3864209649
[56,] 56 1.2893376 268 0.138619021 0.48305040 0.3882533587
[57,] 57 1.3108357 264 0.230118071 0.47916387 0.3951418103
[58,] 58 1.3323339 258 0.097618448 0.47267342 0.3984682241
[59,] 59 1.3538321 250 0.054770570 0.46561671 0.4077477188
[60,] 60 1.3753303 242 0.029636164 0.45835784 0.4211849614
[61,] 61 1.3968285 237 0.009004660 0.45099206 0.4393027329
[62,] 62 1.4183266 228 0.028482166 0.44418405 0.4669123631
[63,] 63 1.4398248 222 0.003855771 0.43719483 0.4866455488
[64,] 64 1.4613230 219 0.016704734 0.43062688 0.5232256495
[65,] 65 1.4828212 215 0.012862827 0.42420102 0.5491914595
[66,] 66 1.5043193 207 0.006533026 0.41787305 0.5783361345
[67,] 67 1.5258175 205 0.041614805 0.41227054 0.6148282135
[68,] 68 1.5473157 198 0.075235246 0.40735798 0.6352254935
[69,] 69 1.5688139 195 0.061106972 0.40236806 0.6502958115
[70,] 70 1.5903121 188 0.040699389 0.39721353 0.6675055714
[71,] 71 1.6118102 182 0.017217618 0.39186358 0.6889022710
[72,] 72 1.6333084 180 0.043514521 0.38703895 0.7193312348
[73,] 73 1.6548066 176 0.037415267 0.38225942 0.7410481257
[74,] 74 1.6763048 169 0.020029116 0.37736716 0.7646889766
[75,] 75 1.6978029 165 0.048298336 0.37299565 0.7954370256
[76,] 76 1.7193011 159 0.096484759 0.36942284 0.8173367839
[77,] 77 1.7407993 156 0.033043579 0.36506153 0.8319290641
[78,] 78 1.7622975 155 0.033428908 0.36081715 0.8584500984
[79,] 79 1.7837957 150 0.040427682 0.35677222 0.8853277489
[80,] 80 1.8052938 143 0.120858749 0.35392269 0.9104962419
[81,] 81 1.8267920 142 0.070997690 0.35046246 0.9233251165
[82,] 82 1.8482902 141 0.104580625 0.34753564 0.9423407809
[83,] 83 1.8697884 140 0.305888372 0.34774753 0.9569773478
[84,] 84 1.8912865 139 0.149704268 0.34553829 0.9591764356
[85,] 85 1.9127847 137 0.283886131 0.34540155 0.9695662773
[86,] 86 1.9342829 135 0.515263194 0.34980560 0.9725939735
[87,] 87 1.9557811 134 0.171797144 0.34795148 0.9688560854
[88,] 88 1.9772793 131 0.391625176 0.34964480 0.9774369939
[89,] 89 1.9987774 130 0.451150166 0.35245700 0.9768050766
[90,] 90 2.0202756 127 0.361805027 0.35353094 0.9746292423
[91,] 91 2.0417738 122 0.800737403 0.36737270 0.9748692965
[92,] 92 2.0632720 121 0.056416140 0.36401072 0.9666305254
[93,] 93 2.0847701 117 0.318906557 0.36422626 0.9865908584
[94,] 94 2.1062683 115 0.716531311 0.37376272 0.9881642416
[95,] 95 2.1277665 113 0.438578026 0.37590503 0.9812359105
[96,] 96 2.1492647 109 0.157299207 0.37377210 0.9794758529
[97,] 97 2.1707629 107 0.317310508 0.37385398 0.9882359862
est.scale est.shape
[1,] 0.9869860 -1.695464e-02
[2,] 0.9857848 -1.642346e-02
[3,] 0.9876135 -1.763330e-02
[4,] 1.0119918 -2.997044e-02
[5,] 1.0050468 -2.684474e-02
[6,] 1.0087172 -2.890263e-02
[7,] 1.0083126 -2.893834e-02
[8,] 1.0169240 -3.365861e-02
[9,] 1.0112141 -3.110787e-02
[10,] 0.9900949 -2.086969e-02
[11,] 1.0009504 -2.672312e-02
[12,] 1.0049530 -2.893283e-02
[13,] 0.9932281 -2.332162e-02
[14,] 0.9877720 -2.084439e-02
[15,] 0.9794885 -1.688411e-02
[16,] 0.9775245 -1.594976e-02
[17,] 0.9703293 -1.241254e-02
[18,] 0.9703334 -1.249945e-02
[19,] 0.9579214 -6.050034e-03
[20,] 0.9654604 -1.028691e-02
[21,] 0.9575381 -6.103116e-03
[22,] 0.9571083 -5.936581e-03
[23,] 0.9579860 -6.386631e-03
[24,] 0.9418044 1.900245e-03
[25,] 0.9251189 1.175473e-02
[26,] 0.9195434 1.510705e-02
[27,] 0.9183290 1.591383e-02
[28,] 0.9500908 -1.864442e-03
[29,] 0.9611586 -7.928693e-03
[30,] 0.9410114 3.056091e-03
[31,] 0.9497055 -1.733228e-03
[32,] 0.9516691 -2.848007e-03
[33,] 0.9417358 2.654858e-03
[34,] 0.9133463 1.904947e-02
[35,] 0.9024326 2.572427e-02
[36,] 0.8870506 3.542522e-02
[37,] 0.8811850 3.956032e-02
[38,] 0.8759034 4.345374e-02
[39,] 0.9027101 2.728255e-02
[40,] 0.9224946 1.572848e-02
[41,] 0.9234297 1.548168e-02
[42,] 0.9256746 1.435142e-02
[43,] 0.9465817 2.381474e-03
[44,] 0.9288118 1.262145e-02
[45,] 0.9224101 1.659336e-02
[46,] 0.9359666 8.780452e-03
[47,] 0.9578192 -3.678858e-03
[48,] 0.9632569 -6.717401e-03
[49,] 0.9702554 -1.064851e-02
[50,] 0.9648317 -7.773212e-03
[51,] 0.9667854 -8.942150e-03
[52,] 0.9774982 -1.500566e-02
[53,] 0.9678597 -9.671053e-03
[54,] 0.9356337 8.599795e-03
[55,] 0.9334798 9.842143e-03
[56,] 0.9310249 1.144449e-02
[57,] 0.9139722 2.204113e-02
[58,] 0.9135134 2.255564e-02
[59,] 0.9307486 1.258940e-02
[60,] 0.9517893 8.965894e-05
[61,] 0.9481225 2.311846e-03
[62,] 0.9830977 -1.775443e-02
[63,] 0.9927850 -2.328413e-02
[64,] 0.9748126 -1.352337e-02
[65,] 0.9666962 -9.131202e-03
[66,] 0.9998984 -2.775774e-02
[67,] 0.9738493 -1.354926e-02
[68,] 1.0011884 -2.895300e-02
[69,] 0.9869151 -2.143642e-02
[70,] 1.0186432 -3.892228e-02
[71,] 1.0423690 -5.186385e-02
[72,] 1.0211857 -4.146645e-02
[73,] 1.0233957 -4.312365e-02
[74,] 1.0641049 -6.440307e-02
[75,] 1.0708668 -6.833835e-02
[76,] 1.1052042 -8.534999e-02
[77,] 1.1022939 -8.499779e-02
[78,] 1.0732475 -7.194576e-02
[79,] 1.0987840 -8.492584e-02
[80,] 1.1550431 -1.109482e-01
[81,] 1.1287621 -1.006135e-01
[82,] 1.1022359 -8.957552e-02
[83,] 1.0745098 -7.723649e-02
[84,] 1.0458809 -6.393696e-02
[85,] 1.0316166 -5.732515e-02
[86,] 1.0176596 -5.083853e-02
[87,] 0.9879054 -3.532169e-02
[88,] 0.9885345 -3.609650e-02
[89,] 0.9574278 -1.875970e-02
[90,] 0.9589417 -1.978602e-02
[91,] 0.9966464 -4.145499e-02
[92,] 0.9668326 -2.517574e-02
[93,] 0.9909773 -3.919662e-02
[94,] 0.9799499 -3.344927e-02
[95,] 0.9698719 -2.796338e-02
[96,] 0.9992297 -4.493423e-02
[97,] 0.9921108 -4.159460e-02
tea documentation built on April 19, 2020, 3:57 p.m.
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Description Usage Arguments Details Value References Examples
Description
An implementation of the sequential testing procedure proposed in Thompson et al. (2009) for automated threshold selection
Usage
1 |
Arguments
data |
vector of sample data |
thresholds |
a sequence of pre-defined thresholds to check for GPD assumption |
Details
The procedure proposed in Thompson et al. (2009) is based on sequential goodness of fit testing. First, one has to choose a equally spaced grid of posssible thresholds. The authors recommend 100 thresholds between the 50 percent and 98 percent quantile of the data, provided there are enough observations left (about 100 observations above the last pre-defined threshold). Then the parameters of a GPD for each threshold are estimated. One can show that the differences of subsequent scale parameters are approximately normal distributed. So a Pearson chi-squared test for normality is applied to all the differences, striking the smallest thresholds out until the test is not rejected anymore.
Value
threshold |
the threshold used for the test |
num.above |
the number of observations above the given threshold |
p.values |
raw p-values for the thresholds tested |
ForwardStop |
transformed p-values according to the ForwardStop criterion. See G'Sell et al (2016) for more information |
StrongStop |
transformed p-values according to the StrongStop criterion. See G'Sell et al (2016) for more information |
est.scale |
estimated scale parameter for the given threshold |
est.shape |
estimated shape parameter for the given threshold |
References
Thompson, P. and Cai, Y. and Reeve, D. (2009). Automated threshold selection methods for extreme wave analysis. Coastal Engineering, 56(10), 1013–1021.
G'Sell, M.G. and Wager, S. and Chouldechova, A. and Tibshirani, R. (2016). Sequential selection procedures and false discovery rate control. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 78(2), 423–444.
Examples
1 2 3 |
Example output
Loading required package: eva
testnum threshold num.above p.values ForwardStop StrongStop
[1,] 1 0.1069378 900 0.020061467 0.02026543 0.0001224283
[2,] 2 0.1284360 881 0.043764781 0.03250839 0.0030513307
[3,] 3 0.1499341 861 0.073231143 0.04702262 0.0097237915
[4,] 4 0.1714323 832 0.032786177 0.04360089 0.0174313744
[5,] 5 0.1929305 817 0.047948401 0.04470792 0.0327716963
[6,] 6 0.2144287 798 0.042195689 0.04444190 0.0501375202
[7,] 7 0.2359269 781 0.068181693 0.04818126 0.0728346516
[8,] 8 0.2574250 761 0.039442099 0.04718873 0.0935330268
[9,] 9 0.2789232 747 0.059978784 0.04881808 0.1245424668
[10,] 10 0.3004214 739 0.083696948 0.05267708 0.1532279569
[11,] 11 0.3219196 719 0.037366046 0.05135026 0.1785148559
[12,] 12 0.3434177 702 0.057975184 0.05204804 0.2206279896
[13,] 13 0.3649159 691 0.100853782 0.05622201 0.2582032218
[14,] 14 0.3864141 678 0.064024295 0.05693228 0.2860329308
[15,] 15 0.4079123 666 0.104700023 0.06050989 0.3248732089
[16,] 16 0.4294105 652 0.122325228 0.06488297 0.3540153196
[17,] 17 0.4509086 640 0.143942088 0.07020852 0.3799473022
[18,] 18 0.4724068 626 0.133124057 0.07424468 0.4021778483
[19,] 19 0.4939050 616 0.187505819 0.08126583 0.4261764668
[20,] 20 0.5154032 600 0.191686741 0.08784281 0.4421559274
[21,] 21 0.5369013 589 0.250574371 0.09739545 0.4573582828
[22,] 22 0.5583995 576 0.281018518 0.10796473 0.4663105346
[23,] 23 0.5798977 563 0.293933848 0.11840307 0.4725280288
[24,] 24 0.6013959 555 0.598819809 0.15152563 0.4775993768
[25,] 25 0.6228941 547 0.498313073 0.17305576 0.4683972226
[26,] 26 0.6443922 536 0.628677920 0.20450306 0.4631065043
[27,] 27 0.6658904 524 0.699593947 0.24147036 0.4539868001
[28,] 28 0.6873886 504 0.706148713 0.27658504 0.4436039467
[29,] 29 0.7088868 490 0.681017434 0.30644828 0.4336626308
[30,] 30 0.7303849 484 0.439071869 0.31550542 0.4247974565
[31,] 31 0.7518831 471 0.465218545 0.32551805 0.4225294148
[32,] 32 0.7733813 460 0.530299574 0.33895999 0.4195554869
[33,] 33 0.7948795 452 0.567515095 0.35408872 0.4149866765
[34,] 34 0.8163777 448 0.501132281 0.36412771 0.4097551363
[35,] 35 0.8378758 440 0.473484843 0.37205192 0.4062189778
[36,] 36 0.8593740 433 0.556991203 0.38433286 0.4034620786
[37,] 37 0.8808722 424 0.611718139 0.39951369 0.3989911537
[38,] 38 0.9023704 415 0.750658833 0.42555105 0.3936862769
[39,] 39 0.9238685 400 0.738140064 0.44899706 0.3864978589
[40,] 40 0.9453667 387 0.606231873 0.46107196 0.3797805901
[41,] 41 0.9668649 378 0.681362473 0.47772145 0.3751828088
[42,] 42 0.9883631 369 0.471370725 0.48152494 0.3696931834
[43,] 43 1.0098613 357 0.358836516 0.48066321 0.3676201928
[44,] 44 1.0313594 352 0.595371752 0.49030238 0.3679309982
[45,] 45 1.0528576 345 0.682140151 0.50487665 0.3640197867
[46,] 46 1.0743558 335 0.583597610 0.51294680 0.3591462784
[47,] 47 1.0958540 324 0.490086522 0.51636312 0.3556442842
[48,] 48 1.1173521 316 0.487005024 0.51951158 0.3535594056
[49,] 49 1.1388503 308 0.445393229 0.52093984 0.3515744228
[50,] 50 1.1603485 302 0.298646343 0.51761590 0.3502771809
[51,] 51 1.1818467 295 0.270720238 0.51365672 0.3518102837
[52,] 52 1.2033449 287 0.057437734 0.50491627 0.3539993032
[53,] 53 1.2248430 282 0.037105950 0.49610298 0.3669369710
[54,] 54 1.2463412 280 0.237422850 0.49193536 0.3832350415
[55,] 55 1.2678394 274 0.286158526 0.48912007 0.3864209649
[56,] 56 1.2893376 268 0.138619021 0.48305040 0.3882533587
[57,] 57 1.3108357 264 0.230118071 0.47916387 0.3951418103
[58,] 58 1.3323339 258 0.097618448 0.47267342 0.3984682241
[59,] 59 1.3538321 250 0.054770570 0.46561671 0.4077477188
[60,] 60 1.3753303 242 0.029636164 0.45835784 0.4211849614
[61,] 61 1.3968285 237 0.009004660 0.45099206 0.4393027329
[62,] 62 1.4183266 228 0.028482166 0.44418405 0.4669123631
[63,] 63 1.4398248 222 0.003855771 0.43719483 0.4866455488
[64,] 64 1.4613230 219 0.016704734 0.43062688 0.5232256495
[65,] 65 1.4828212 215 0.012862827 0.42420102 0.5491914595
[66,] 66 1.5043193 207 0.006533026 0.41787305 0.5783361345
[67,] 67 1.5258175 205 0.041614805 0.41227054 0.6148282135
[68,] 68 1.5473157 198 0.075235246 0.40735798 0.6352254935
[69,] 69 1.5688139 195 0.061106972 0.40236806 0.6502958115
[70,] 70 1.5903121 188 0.040699389 0.39721353 0.6675055714
[71,] 71 1.6118102 182 0.017217618 0.39186358 0.6889022710
[72,] 72 1.6333084 180 0.043514521 0.38703895 0.7193312348
[73,] 73 1.6548066 176 0.037415267 0.38225942 0.7410481257
[74,] 74 1.6763048 169 0.020029116 0.37736716 0.7646889766
[75,] 75 1.6978029 165 0.048298336 0.37299565 0.7954370256
[76,] 76 1.7193011 159 0.096484759 0.36942284 0.8173367839
[77,] 77 1.7407993 156 0.033043579 0.36506153 0.8319290641
[78,] 78 1.7622975 155 0.033428908 0.36081715 0.8584500984
[79,] 79 1.7837957 150 0.040427682 0.35677222 0.8853277489
[80,] 80 1.8052938 143 0.120858749 0.35392269 0.9104962419
[81,] 81 1.8267920 142 0.070997690 0.35046246 0.9233251165
[82,] 82 1.8482902 141 0.104580625 0.34753564 0.9423407809
[83,] 83 1.8697884 140 0.305888372 0.34774753 0.9569773478
[84,] 84 1.8912865 139 0.149704268 0.34553829 0.9591764356
[85,] 85 1.9127847 137 0.283886131 0.34540155 0.9695662773
[86,] 86 1.9342829 135 0.515263194 0.34980560 0.9725939735
[87,] 87 1.9557811 134 0.171797144 0.34795148 0.9688560854
[88,] 88 1.9772793 131 0.391625176 0.34964480 0.9774369939
[89,] 89 1.9987774 130 0.451150166 0.35245700 0.9768050766
[90,] 90 2.0202756 127 0.361805027 0.35353094 0.9746292423
[91,] 91 2.0417738 122 0.800737403 0.36737270 0.9748692965
[92,] 92 2.0632720 121 0.056416140 0.36401072 0.9666305254
[93,] 93 2.0847701 117 0.318906557 0.36422626 0.9865908584
[94,] 94 2.1062683 115 0.716531311 0.37376272 0.9881642416
[95,] 95 2.1277665 113 0.438578026 0.37590503 0.9812359105
[96,] 96 2.1492647 109 0.157299207 0.37377210 0.9794758529
[97,] 97 2.1707629 107 0.317310508 0.37385398 0.9882359862
est.scale est.shape
[1,] 0.9869860 -1.695464e-02
[2,] 0.9857848 -1.642346e-02
[3,] 0.9876135 -1.763330e-02
[4,] 1.0119918 -2.997044e-02
[5,] 1.0050468 -2.684474e-02
[6,] 1.0087172 -2.890263e-02
[7,] 1.0083126 -2.893834e-02
[8,] 1.0169240 -3.365861e-02
[9,] 1.0112141 -3.110787e-02
[10,] 0.9900949 -2.086969e-02
[11,] 1.0009504 -2.672312e-02
[12,] 1.0049530 -2.893283e-02
[13,] 0.9932281 -2.332162e-02
[14,] 0.9877720 -2.084439e-02
[15,] 0.9794885 -1.688411e-02
[16,] 0.9775245 -1.594976e-02
[17,] 0.9703293 -1.241254e-02
[18,] 0.9703334 -1.249945e-02
[19,] 0.9579214 -6.050034e-03
[20,] 0.9654604 -1.028691e-02
[21,] 0.9575381 -6.103116e-03
[22,] 0.9571083 -5.936581e-03
[23,] 0.9579860 -6.386631e-03
[24,] 0.9418044 1.900245e-03
[25,] 0.9251189 1.175473e-02
[26,] 0.9195434 1.510705e-02
[27,] 0.9183290 1.591383e-02
[28,] 0.9500908 -1.864442e-03
[29,] 0.9611586 -7.928693e-03
[30,] 0.9410114 3.056091e-03
[31,] 0.9497055 -1.733228e-03
[32,] 0.9516691 -2.848007e-03
[33,] 0.9417358 2.654858e-03
[34,] 0.9133463 1.904947e-02
[35,] 0.9024326 2.572427e-02
[36,] 0.8870506 3.542522e-02
[37,] 0.8811850 3.956032e-02
[38,] 0.8759034 4.345374e-02
[39,] 0.9027101 2.728255e-02
[40,] 0.9224946 1.572848e-02
[41,] 0.9234297 1.548168e-02
[42,] 0.9256746 1.435142e-02
[43,] 0.9465817 2.381474e-03
[44,] 0.9288118 1.262145e-02
[45,] 0.9224101 1.659336e-02
[46,] 0.9359666 8.780452e-03
[47,] 0.9578192 -3.678858e-03
[48,] 0.9632569 -6.717401e-03
[49,] 0.9702554 -1.064851e-02
[50,] 0.9648317 -7.773212e-03
[51,] 0.9667854 -8.942150e-03
[52,] 0.9774982 -1.500566e-02
[53,] 0.9678597 -9.671053e-03
[54,] 0.9356337 8.599795e-03
[55,] 0.9334798 9.842143e-03
[56,] 0.9310249 1.144449e-02
[57,] 0.9139722 2.204113e-02
[58,] 0.9135134 2.255564e-02
[59,] 0.9307486 1.258940e-02
[60,] 0.9517893 8.965894e-05
[61,] 0.9481225 2.311846e-03
[62,] 0.9830977 -1.775443e-02
[63,] 0.9927850 -2.328413e-02
[64,] 0.9748126 -1.352337e-02
[65,] 0.9666962 -9.131202e-03
[66,] 0.9998984 -2.775774e-02
[67,] 0.9738493 -1.354926e-02
[68,] 1.0011884 -2.895300e-02
[69,] 0.9869151 -2.143642e-02
[70,] 1.0186432 -3.892228e-02
[71,] 1.0423690 -5.186385e-02
[72,] 1.0211857 -4.146645e-02
[73,] 1.0233957 -4.312365e-02
[74,] 1.0641049 -6.440307e-02
[75,] 1.0708668 -6.833835e-02
[76,] 1.1052042 -8.534999e-02
[77,] 1.1022939 -8.499779e-02
[78,] 1.0732475 -7.194576e-02
[79,] 1.0987840 -8.492584e-02
[80,] 1.1550431 -1.109482e-01
[81,] 1.1287621 -1.006135e-01
[82,] 1.1022359 -8.957552e-02
[83,] 1.0745098 -7.723649e-02
[84,] 1.0458809 -6.393696e-02
[85,] 1.0316166 -5.732515e-02
[86,] 1.0176596 -5.083853e-02
[87,] 0.9879054 -3.532169e-02
[88,] 0.9885345 -3.609650e-02
[89,] 0.9574278 -1.875970e-02
[90,] 0.9589417 -1.978602e-02
[91,] 0.9966464 -4.145499e-02
[92,] 0.9668326 -2.517574e-02
[93,] 0.9909773 -3.919662e-02
[94,] 0.9799499 -3.344927e-02
[95,] 0.9698719 -2.796338e-02
[96,] 0.9992297 -4.493423e-02
[97,] 0.9921108 -4.159460e-02
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