Matlab FX_DS_AZ_LOOP Looped Grid Solution for the Stationary Distribution of Optimal Savings Dynamic Programming Problem
Fan Wang
2020-07-25
1 FF_DS_AZ_LOOP Dynamic Savings Loop Discrete Distribution
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Examples](https://fanwangecon.github.io/M4Econ/), or** Dynamic Asset This is the example vignette for function: ff_ds_az_loop from the MEconTools Package. F(a,z) discrete probability mass function given policy function solution with discretized savings choices.
Distribution for Common Choice and States Grid Loop: ff_ds_az_cts_loop
Distribution for States Grid + Continuous Exact Savings as Share of Cash-on-Hand Loop: ff_ds_az_cts_loop
Distribution for States Grid + Continuous Exact Savings as Share of Cash-on-Hand Vectorized: ff_ds_az_cts_vec
1.1 Test FF_DS_AZ_LOOP Defaults
Call the function with defaults. By default, shows the asset policy function summary. Model parameters can be changed by the mp_params.
%mp_params
mp_params = containers.Map('KeyType','char', 'ValueType','any');
mp_params('fl_crra') = 1.5;
mp_params('fl_beta') = 0.94;
% call function
ff_ds_az_loop(mp_params);
Elapsed time is 0.191238 seconds.
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
CONTAINER NAME: mp_ffcmd ND Array (Matrix etc)
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i idx ndim numel rowN colN sum mean std coefvari min max
_ ___ ____ _____ ____ ____ ______ ______ ______ ________ ___ ___
ap 1 1 2 700 100 7 9855.1 14.079 14.408 1.0234 0 50
xxx TABLE:ap xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4 c5 c6 c7
______ ______ ______ ________ _______ _______ ______
r1 0 0 0 0.045213 0.25576 0.61095 1.0362
r2 0 0 0 0.045213 0.25576 0.61095 1.0362
r3 0 0 0 0.045213 0.25576 0.61095 1.0362
r4 0 0 0 0.06647 0.25576 0.61095 1.0362
r5 0 0 0 0.06647 0.25576 0.61095 1.164
r96 43.924 43.924 43.924 43.924 43.924 45.102 45.102
r97 45.102 45.102 45.102 45.102 45.102 46.298 46.298
r98 46.298 46.298 46.298 46.298 46.298 47.513 47.513
r99 47.513 47.513 47.513 47.513 47.513 48.747 48.747
r100 48.747 48.747 48.747 48.747 48.747 50 50
FF_DS_AZ_LOOP finished. Distribution took = 0.14487
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
CONTAINER NAME: mp_ddcmd ND Array (Matrix etc)
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
i idx ndim numel rowN colN sum mean std coefvari min max
_ ___ ____ _____ ____ ____ ___ _________ _________ ________ ________ ________
fa 1 1 2 100 100 1 1 0.01 0.016114 1.6114 0 0.121
faz 2 2 2 700 100 7 1 0.0014286 0.0035847 2.5093 0 0.052693
fz 3 3 2 7 7 1 1 0.14286 0.11742 0.82196 0.015625 0.3125
xxx TABLE:fa xxxxxxxxxxxxxxxxxx
c1
__________
r1 0.121
r2 0.00034068
r3 0
r4 0.010458
r5 0.0048751
r96 1.1148e-21
r97 3.227e-22
r98 7.9165e-23
r99 1.4982e-23
r100 1.7037e-24
xxx TABLE:faz xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4 c5 c6 c7
__________ __________ __________ __________ __________ __________ __________
r1 0.0084023 0.03778 0.052693 0.018985 0.0029243 0.00020787 5.6301e-06
r2 0.00018105 0.0001207 3.3528e-05 4.9671e-06 4.1392e-07 1.8397e-08 3.4068e-10
r3 0 0 0 0 0 0 0
r4 0.00016518 0.002081 0.005593 0.0022334 0.00035834 2.6032e-05 7.146e-07
r5 0.00021881 0.00067299 0.0026761 0.0011123 0.00018127 1.3278e-05 3.6641e-07
r96 1.7183e-25 2.8942e-24 2.2565e-23 1.0675e-22 3.1764e-22 4.9586e-22 1.6895e-22
r97 3.2228e-26 6.111e-25 5.3384e-24 2.7969e-23 9.0055e-23 1.4769e-22 5.1004e-23
r98 4.5065e-27 1.0023e-25 1.0174e-24 6.0677e-24 2.15e-23 3.7371e-23 1.3103e-23
r99 3.8775e-28 1.0954e-26 1.38e-25 9.8022e-25 3.9213e-24 7.3193e-24 2.6118e-24
r100 1.1692e-29 5.3148e-28 9.7109e-27 8.9563e-26 4.2252e-25 8.6574e-25 3.1562e-25
xxx TABLE:fz xxxxxxxxxxxxxxxxxx
c1
________
r1 0.015625
r2 0.09375
r3 0.23438
r4 0.3125
r5 0.23438
r6 0.09375
r7 0.015625
1.2 Test FF_DS_AZ_LOOP Speed Tests
Call the function with different a and z grid size, print out speed:
mp_support = containers.Map('KeyType','char', 'ValueType','any');
mp_support('bl_timer') = true;
mp_support('ls_ffcmd') = {};
mp_support('ls_ddcmd') = {};
mp_support('ls_ddgrh') = {};
mp_support('bl_show_stats_table') = false;
% A grid 50, shock grid 5:
mp_params = containers.Map('KeyType','char', 'ValueType','any');
mp_params('it_a_n') = 50;
mp_params('it_z_n') = 5;
ff_ds_az_loop(mp_params, mp_support);
Elapsed time is 0.021787 seconds.
FF_DS_AZ_LOOP finished. Distribution took = 0.046636
% A grid 100, shock grid 7:
mp_params = containers.Map('KeyType','char', 'ValueType','any');
mp_params('it_a_n') = 100;
mp_params('it_z_n') = 7;
ff_ds_az_loop(mp_params, mp_support);
Elapsed time is 0.218465 seconds.
FF_DS_AZ_LOOP finished. Distribution took = 0.13608
% A grid 200, shock grid 9:
mp_params = containers.Map('KeyType','char', 'ValueType','any');
mp_params('it_a_n') = 200;
mp_params('it_z_n') = 9;
ff_ds_az_loop(mp_params, mp_support);
Elapsed time is 0.489370 seconds.
FF_DS_AZ_LOOP finished. Distribution took = 0.353931.3 Test FF_DS_AZ_LOOP A grid 100 Shock grid 7
Call the function with different a and z grid size, print out speed:
mp_support = containers.Map('KeyType','char', 'ValueType','any');
mp_support('bl_timer') = true;
mp_support('ls_ffcmd') = {};
mp_support('ls_ddcmd') = {};
mp_support('ls_ddgrh') = {'faz','fa'};
mp_support('bl_show_stats_table') = true;
mp_params = containers.Map('KeyType','char', 'ValueType','any');
mp_params('it_a_n') = 100;
mp_params('it_z_n') = 7;
ff_ds_az_loop(mp_params, mp_support);
Elapsed time is 0.217312 seconds.
FF_DS_AZ_LOOP finished. Distribution took = 0.1105
xxx tb_outcomes: all stats xxx
OriginalVariableNames ap v c y coh savefraccoh
______________________ __________ __________ __________ __________ __________ ___________
{'mean' } 2.7094 6.6576 1.5089 1.5084 4.2183 0.48487
{'unweighted_sum' } 1439.4 7299.4 1545.9 1473.6 11549 479.94
{'sd' } 2.8976 2.0599 0.35843 0.52611 3.2096 0.25477
{'coefofvar' } 1.0694 0.3094 0.23755 0.34879 0.76088 0.52544
{'gini' } 0.53346 0.17414 0.13326 0.19097 0.39103 0.29771
{'min' } 0 1.6927 0.58543 0.58543 0.58543 0
{'max' } 50 19.139 4.9969 4.9969 54.997 0.93121
{'pYis0' } 0.070216 0 0 0 0 0.070216
{'pYls0' } 0 0 0 0 0 0
{'pYgr0' } 0.92978 1 1 1 1 0.92978
{'pYisMINY' } 0.070216 0.0057675 0.0057675 0.0057675 0.0057675 0.070216
{'pYisMAXY' } 2.1143e-10 3.7149e-11 3.7149e-11 3.7149e-11 3.7149e-11 2.065e-11
{'p0_01' } 0 1.6927 0.58543 0.58543 0.58543 0
{'p0_1' } 0 1.6927 0.58543 0.58543 0.58543 0
{'p1' } 0 2.7674 0.76855 0.61362 0.76855 0
{'p5' } 0 3.273 0.91608 0.77504 1.009 0
{'p10' } 0.06647 4.0961 1.0308 0.92803 1.1055 0.067651
{'p20' } 0.37601 4.8781 1.2371 1.0319 1.555 0.22796
{'p25' } 0.52503 5.2636 1.2781 1.0731 1.8354 0.28067
{'p30' } 0.7048 5.4822 1.3424 1.1472 2.0866 0.35907
{'p40' } 1.3008 6.0574 1.3953 1.3424 2.6774 0.48584
{'p50' } 1.9422 6.542 1.4931 1.4023 3.3444 0.54915
{'p60' } 2.5275 7.1265 1.6174 1.4954 4.1208 0.60499
{'p70' } 3.456 7.657 1.6502 1.7803 5.1554 0.67918
{'p75' } 3.9869 8.0469 1.733 1.824 5.7555 0.69673
{'p80' } 4.564 8.4125 1.8179 1.8875 6.1793 0.72076
{'p90' } 6.5844 9.3821 1.9734 2.3349 8.568 0.76882
{'p95' } 8.1844 10.225 2.1388 2.4776 10.358 0.80411
{'p99' } 13.136 11.834 2.3359 3.1677 15.511 0.85404
{'p99_9' } 18.839 13.486 2.7733 3.4782 21.332 0.88316
{'p99_99' } 21.778 14.354 3.0939 3.7505 24.78 0.89063
{'fl_cov_ap' } 8.396 5.2587 0.88866 0.93721 9.2847 0.58458
{'fl_cor_ap' } 1 0.88106 0.85565 0.61478 0.99833 0.7919
{'fl_cov_v' } 5.2587 4.243 0.71989 0.93806 5.9786 0.453
{'fl_cor_v' } 0.88106 1 0.97505 0.86559 0.90428 0.86321
{'fl_cov_c' } 0.88866 0.71989 0.12847 0.15253 1.0171 0.079518
{'fl_cor_c' } 0.85565 0.97505 1 0.80886 0.88413 0.8708
{'fl_cov_y' } 0.93721 0.93806 0.15253 0.2768 1.0897 0.080824
{'fl_cor_y' } 0.61478 0.86559 0.80886 1 0.64534 0.603
{'fl_cov_coh' } 9.2847 5.9786 1.0171 1.0897 10.302 0.6641
{'fl_cor_coh' } 0.99833 0.90428 0.88413 0.64534 1 0.81215
{'fl_cov_savefraccoh'} 0.58458 0.453 0.079518 0.080824 0.6641 0.064906
{'fl_cor_savefraccoh'} 0.7919 0.86321 0.8708 0.603 0.81215 1
{'fracByP0_01' } 0 0.0014664 0.0022377 0.0022385 0.00080043 0
{'fracByP0_1' } 0 0.0014664 0.0022377 0.0022385 0.00080043 0
{'fracByP1' } 0 0.0029302 0.01567 0.00403 0.0055106 0
{'fracByP5' } 0 0.021763 0.026172 0.02466 0.015702 0
{'fracByP10' } 0.0004071 0.050764 0.058937 0.05144 0.022123 0.0021411
{'fracByP20' } 0.0096198 0.1171 0.13549 0.11855 0.05416 0.033082
{'fracByP25' } 0.017608 0.15851 0.17677 0.15694 0.074837 0.057303
{'fracByP30' } 0.02761 0.19906 0.21973 0.19018 0.09783 0.092029
{'fracByP40' } 0.071719 0.28454 0.3135 0.28477 0.15542 0.18016
{'fracByP50' } 0.15388 0.38017 0.40577 0.38385 0.23227 0.28549
{'fracByP60' } 0.21684 0.48325 0.51534 0.46249 0.31381 0.4039
{'fracByP70' } 0.32573 0.59393 0.62048 0.57438 0.42716 0.54543
{'fracByP75' } 0.39815 0.65416 0.68002 0.63899 0.4882 0.60905
{'fracByP80' } 0.48482 0.72413 0.732 0.69931 0.55881 0.6822
{'fracByP90' } 0.6819 0.84902 0.85906 0.8281 0.73338 0.83355
{'fracByP95' } 0.79123 0.91664 0.92592 0.90812 0.83969 0.91574
{'fracByP99' } 0.9433 0.98136 0.98418 0.97889 0.95655 0.98225
{'fracByP99_9' } 0.99595 0.99805 0.99819 0.99776 0.99501 0.99858
{'fracByP99_99' } 0.99934 0.99982 0.99985 0.9998 0.99938 0.99984 1.4 Test FF_DS_AZ_LOOP A grid 300 Shock Grid 25
mp_support = containers.Map('KeyType','char', 'ValueType','any');
mp_support('bl_timer') = true;
mp_support('ls_ffcmd') = {};
mp_support('ls_ddcmd') = {};
mp_support('ls_ddgrh') = {'faz','fa'};
mp_support('bl_show_stats_table') = true;
mp_params = containers.Map('KeyType','char', 'ValueType','any');
mp_params('it_a_n') = 300;
mp_params('it_z_n') = 25;
ff_ds_az_loop(mp_params, mp_support);
Elapsed time is 1.356902 seconds.
FF_DS_AZ_LOOP finished. Distribution took = 1.3706
xxx tb_outcomes: all stats xxx
OriginalVariableNames ap v c y coh savefraccoh
______________________ __________ __________ __________ __________ __________ ___________
{'mean' } 3.1835 6.9106 1.5286 1.5274 4.7121 0.52236
{'unweighted_sum' } 4296.5 79518 16864 19751 1.2716e+05 5295.3
{'sd' } 3.2831 2.152 0.35175 0.53521 3.5973 0.25161
{'coefofvar' } 1.0313 0.31141 0.2301 0.35041 0.76341 0.48168
{'gini' } 0.52466 0.17565 0.12887 0.19155 0.39536 0.26998
{'min' } 0 -2.7621 0.25871 0.25871 0.25871 0
{'max' } 50 20.027 8.7798 8.7798 58.78 0.93152
{'pYis0' } 0.050267 0 0 0 0 0.050267
{'pYls0' } 0 7.4299e-05 0 0 0 0
{'pYgr0' } 0.94973 0.99993 1 1 1 0.94973
{'pYisMINY' } 0.050267 3.1587e-08 3.1587e-08 3.1587e-08 3.1587e-08 0.050267
{'pYisMAXY' } 2.3964e-09 9.6288e-14 9.6288e-14 9.6288e-14 9.6288e-14 2.6173e-22
{'p0_01' } 0 0.33524 0.44588 0.42089 0.44588 0
{'p0_1' } 0 1.0281 0.51088 0.51088 0.51088 0
{'p1' } 0 2.3294 0.67069 0.67069 0.67069 0
{'p5' } 0 3.531 0.9348 0.80006 1.0088 0
{'p10' } 0.10107 4.1808 1.0877 0.90775 1.2209 0.086874
{'p20' } 0.48982 5.0629 1.248 1.0638 1.7564 0.28154
{'p25' } 0.7256 5.3749 1.3048 1.157 2.0452 0.35473
{'p30' } 0.97897 5.7085 1.3561 1.192 2.3425 0.4186
{'p40' } 1.5756 6.2702 1.4389 1.3331 2.9951 0.51678
{'p50' } 2.2184 6.8025 1.5235 1.4352 3.7422 0.59639
{'p60' } 2.9972 7.3608 1.6237 1.5724 4.6044 0.65168
{'p70' } 4.012 7.977 1.7017 1.7487 5.6899 0.7051
{'p75' } 4.5871 8.3254 1.7349 1.8191 6.3522 0.72563
{'p80' } 5.3173 8.7116 1.8227 1.9222 7.1504 0.74857
{'p90' } 7.5009 9.7584 1.9829 2.2334 9.526 0.79537
{'p95' } 9.6743 10.633 2.1133 2.5088 11.809 0.82382
{'p99' } 14.854 12.286 2.3901 3.1545 17.176 0.86207
{'p99_9' } 21.166 14.023 2.7913 3.9726 23.779 0.88709
{'p99_99' } 26.803 15.357 3.0931 4.7968 29.914 0.89989
{'fl_cov_ap' } 10.779 6.2944 1.019 1.0643 11.798 0.64446
{'fl_cor_ap' } 1 0.89089 0.88234 0.60566 0.99894 0.78015
{'fl_cov_v' } 6.2944 4.6311 0.7528 0.97564 7.0472 0.46366
{'fl_cor_v' } 0.89089 1 0.9945 0.84708 0.91033 0.85631
{'fl_cov_c' } 1.019 0.7528 0.12373 0.15568 1.1427 0.077608
{'fl_cor_c' } 0.88234 0.9945 1 0.82696 0.90306 0.8769
{'fl_cov_y' } 1.0643 0.97564 0.15568 0.28645 1.2199 0.077311
{'fl_cor_y' } 0.60566 0.84708 0.82696 1 0.63363 0.57411
{'fl_cov_coh' } 11.798 7.0472 1.1427 1.2199 12.941 0.72207
{'fl_cor_coh' } 0.99894 0.91033 0.90306 0.63363 1 0.79776
{'fl_cov_savefraccoh'} 0.64446 0.46366 0.077608 0.077311 0.72207 0.063308
{'fl_cor_savefraccoh'} 0.78015 0.85631 0.8769 0.57411 0.79776 1
{'fracByP0_01' } 0 7.366e-06 9.1288e-05 2.5324e-05 2.9613e-05 0
{'fracByP0_1' } 0 0.00015226 0.00040756 0.00048297 0.00013202 0
{'fracByP1' } 0 0.0031657 0.0040997 0.0058265 0.0013172 0
{'fracByP5' } 0 0.020854 0.026015 0.023308 0.010613 0
{'fracByP10' } 0.0007829 0.049187 0.059665 0.051833 0.020313 0.0040897
{'fracByP20' } 0.010458 0.1169 0.13673 0.11782 0.052147 0.04121
{'fracByP25' } 0.020375 0.15489 0.17838 0.15407 0.072616 0.071271
{'fracByP30' } 0.033945 0.19501 0.22212 0.1924 0.09561 0.10878
{'fracByP40' } 0.076084 0.28102 0.3131 0.2752 0.15182 0.19951
{'fracByP50' } 0.13323 0.3766 0.41016 0.36618 0.22332 0.30599
{'fracByP60' } 0.21876 0.4783 0.51311 0.46472 0.31143 0.42495
{'fracByP70' } 0.32789 0.58936 0.62182 0.57246 0.4201 0.55532
{'fracByP75' } 0.39329 0.64823 0.67676 0.63063 0.48449 0.62358
{'fracByP80' } 0.47094 0.70976 0.73532 0.69204 0.55555 0.694
{'fracByP90' } 0.66575 0.84269 0.85851 0.82742 0.72907 0.84261
{'fracByP95' } 0.8001 0.91584 0.92543 0.90488 0.84038 0.91895
{'fracByP99' } 0.94734 0.98115 0.98337 0.97713 0.95746 0.98325
{'fracByP99_9' } 0.99324 0.99789 0.99809 0.99717 0.99445 0.9983
{'fracByP99_99' } 0.99909 0.99977 0.99979 0.99967 0.99931 0.99983 1.5 Test FF_DS_AZ_LOOP A grid 300 Shock Grid 50
mp_support = containers.Map('KeyType','char', 'ValueType','any');
mp_support('bl_timer') = true;
mp_support('ls_ffcmd') = {};
mp_support('ls_ddcmd') = {};
mp_support('ls_ddgrh') = {'faz','fa'};
mp_support('bl_show_stats_table') = true;
mp_params = containers.Map('KeyType','char', 'ValueType','any');
mp_params('it_a_n') = 300;
mp_params('it_z_n') = 50;
ff_ds_az_loop(mp_params, mp_support);
Elapsed time is 3.256673 seconds.
FF_DS_AZ_LOOP finished. Distribution took = 3.3311
xxx tb_outcomes: all stats xxx
OriginalVariableNames ap v c y coh savefraccoh
______________________ __________ __________ __________ __________ __________ ___________
{'mean' } 3.26 6.9484 1.5319 1.5305 4.7919 0.52772
{'unweighted_sum' } 4296.5 1.6217e+05 35821 53309 2.6813e+05 10814
{'sd' } 3.3166 2.1606 0.35167 0.5364 3.6315 0.25217
{'coefofvar' } 1.0174 0.31094 0.22956 0.35048 0.75783 0.47785
{'gini' } 0.52112 0.17551 0.12829 0.19134 0.39468 0.26727
{'min' } 0 -7.6871 0.12843 0.12843 0.12843 0
{'max' } 50 20.751 15.657 15.657 65.657 0.93164
{'pYis0' } 0.049546 0 0 0 0 0.049546
{'pYls0' } 0 0.00011924 0 0 0 0
{'pYgr0' } 0.95045 0.99988 1 1 1 0.95045
{'pYisMINY' } 0.049546 1.1021e-15 1.1021e-15 1.1021e-15 1.1021e-15 0.049546
{'pYisMAXY' } 5.1436e-09 3.0978e-19 3.0978e-19 3.0978e-19 3.0978e-19 7.4151e-23
{'p0_01' } 0 -0.20486 0.40271 0.40271 0.40271 0
{'p0_1' } 0 1.2135 0.53589 0.488 0.53589 0
{'p1' } 0 2.3687 0.71312 0.64833 0.71312 0
{'p5' } 0.00050419 3.5428 0.94895 0.8071 0.96945 0.00055062
{'p10' } 0.11149 4.2401 1.0944 0.93681 1.2484 0.095151
{'p20' } 0.51629 5.0791 1.255 1.072 1.7729 0.28687
{'p25' } 0.75904 5.4237 1.3033 1.1504 2.067 0.36257
{'p30' } 1.0189 5.7339 1.3518 1.2006 2.3841 0.42942
{'p40' } 1.6286 6.2919 1.446 1.3198 3.0593 0.53021
{'p50' } 2.2834 6.8389 1.5355 1.4423 3.8053 0.59978
{'p60' } 3.0751 7.4137 1.613 1.5765 4.7113 0.65858
{'p70' } 4.1046 8.0318 1.7011 1.7318 5.8286 0.70939
{'p75' } 4.7891 8.3723 1.7435 1.8266 6.5055 0.73443
{'p80' } 5.5379 8.765 1.8035 1.9295 7.3201 0.75699
{'p90' } 7.6355 9.7879 1.9921 2.2457 9.6214 0.79808
{'p95' } 9.8311 10.68 2.1096 2.5308 11.976 0.82663
{'p99' } 14.653 12.305 2.407 3.1554 17.087 0.86199
{'p99_9' } 21.166 14.067 2.7771 4.0255 23.953 0.88705
{'p99_99' } 27.382 15.467 3.1325 4.887 30.554 0.90105
{'fl_cov_ap' } 11 6.3988 1.032 1.0771 12.032 0.65387
{'fl_cor_ap' } 1 0.89298 0.88481 0.60546 0.99898 0.78182
{'fl_cov_v' } 6.3988 4.668 0.75538 0.97839 7.1542 0.46619
{'fl_cor_v' } 0.89298 1 0.99418 0.84423 0.91183 0.85567
{'fl_cov_c' } 1.032 0.75538 0.12367 0.15613 1.1557 0.077331
{'fl_cor_c' } 0.88481 0.99418 1 0.82768 0.90493 0.87203
{'fl_cov_y' } 1.0771 0.97839 0.15613 0.28772 1.2333 0.076912
{'fl_cor_y' } 0.60546 0.84423 0.82768 1 0.63312 0.56861
{'fl_cov_coh' } 12.032 7.1542 1.1557 1.2333 13.188 0.7312
{'fl_cor_coh' } 0.99898 0.91183 0.90493 0.63312 1 0.79848
{'fl_cov_savefraccoh'} 0.65387 0.46619 0.077331 0.076912 0.7312 0.063589
{'fl_cor_savefraccoh'} 0.78182 0.85567 0.87203 0.56861 0.79848 1
{'fracByP0_01' } 0 -7.082e-06 2.6291e-05 3.0744e-05 8.4044e-06 0
{'fracByP0_1' } 0 8.1705e-05 0.00058298 0.00029929 0.00018591 0
{'fracByP1' } 0 0.0025872 0.0055744 0.0043199 0.0017463 0
{'fracByP5' } 5.9482e-08 0.02063 0.028475 0.023256 0.0085179 3.9707e-07
{'fracByP10' } 0.00083251 0.049013 0.059787 0.051875 0.020182 0.004399
{'fracByP20' } 0.01069 0.11692 0.13707 0.11785 0.051473 0.041367
{'fracByP25' } 0.021006 0.15459 0.17869 0.15432 0.071586 0.072106
{'fracByP30' } 0.034297 0.19493 0.22235 0.19226 0.095063 0.10998
{'fracByP40' } 0.076942 0.2811 0.31433 0.27537 0.15173 0.20135
{'fracByP50' } 0.13547 0.37553 0.41049 0.36597 0.22294 0.30799
{'fracByP60' } 0.21688 0.47822 0.51321 0.46464 0.31179 0.42743
{'fracByP70' } 0.32617 0.58918 0.6213 0.57279 0.42106 0.55684
{'fracByP75' } 0.40001 0.64825 0.67795 0.6311 0.48455 0.62544
{'fracByP80' } 0.47816 0.71036 0.73507 0.69272 0.55654 0.69664
{'fracByP90' } 0.67319 0.84299 0.85862 0.82739 0.73089 0.84294
{'fracByP95' } 0.80347 0.91616 0.92515 0.90483 0.84244 0.91987
{'fracByP99' } 0.94675 0.98117 0.98325 0.97691 0.95831 0.98345
{'fracByP99_9' } 0.99284 0.99789 0.9981 0.99713 0.99445 0.99831
{'fracByP99_99' } 0.99909 0.99977 0.99979 0.99966 0.9993 0.99983