Chapter 4 Distributional Analysis
4.1 FF_SIMU_STATS Examples
Go back to fan’s MEconTools Toolbox (bookdown), Matlab Code Examples Repository (bookdown), or Math for Econ with Matlab Repository (bookdown).
Examples](https://fanwangecon.github.io/M4Econ/), or** Dynamic Asset This is the example vignette for function: ff_simu_stats from the MEconTools Package. This is a gate-way function that computes mean, percentiles, covariance etc between several variables.
4.1.1 Test FF_SIMU_STATS Defaults
Call the function with defaults.
ff_simu_stats();
xxx tb_outcomes: all stats xxx
OriginalVariableNames cl_mt_pol_a cl_mt_pol_c
______________________ ___________ ___________
{'mean' } -0.11081 8.8423
{'sd' } 4.1239 6.5845
{'coefofvar' } -37.215 0.74466
{'min' } -7 -6.3772
{'max' } 9 21.786
{'pYis0' } 0.064259 0
{'pYls0' } 0.54867 0.027329
{'pYgr0' } 0.38707 0.97267
{'pYisMINY' } 0.051764 0.015232
{'pYisMAXY' } 0.027329 0.046484
{'p1' } -7 -6.3772
{'p10' } -6 0.27238
{'p25' } -3 5.2138
{'p50' } -1 6.5321
{'p75' } 3 13.799
{'p90' } 5 16.887
{'p99' } 9 21.786
{'fl_cov_cl_mt_pol_a'} 17.007 -22.084
{'fl_cor_cl_mt_pol_a'} 1 -0.81327
{'fl_cov_cl_mt_pol_c'} -22.084 43.356
{'fl_cor_cl_mt_pol_c'} -0.81327 1
{'fracByP1' } 3.2699 -0.010985
{'fracByP10' } 5.9889 -0.013362
{'fracByP25' } 14.165 0.041007
{'fracByP50' } 16.208 0.1893
{'fracByP75' } 12.702 0.59539
{'fracByP90' } 6.6611 0.8307
{'fracByP99' } 1 1 4.1.2 Test FF_SIMU_STATS Four States-Points Matrix
Over some (a,z) states that is 3 by 3, c matrix, generate all stats
% Set Parameters
mt_x_of_s = [1, 2, 3.0;...
3, 1, 1.5;...
4, 3, 2.0];
mt_y_of_s = [2, -10, 9.0;...
5, 1.1,3.0;...
1, 3, -1.5];
mt_z_of_s = [1.1, 2,3.3;...
2.3, 1,1.5;...
4, 2.5,2.0];
mp_cl_mt_xyz_of_s = containers.Map('KeyType','char', 'ValueType','any');
mp_cl_mt_xyz_of_s('cl_mt_x_of_s') = {mt_x_of_s, zeros(1)};
mp_cl_mt_xyz_of_s('cl_mt_y_of_s') = {mt_y_of_s, zeros(1)};
mp_cl_mt_xyz_of_s('cl_mt_z_of_s') = {mt_z_of_s, zeros(1)};
mp_cl_mt_xyz_of_s('ar_st_y_name') = ["cl_mt_x_of_s", "cl_mt_y_of_s", "cl_mt_z_of_s"];
% Mass
rng(123);
mt_f_of_s = rand(size(mt_x_of_s));
mt_f_of_s = mt_f_of_s/sum(mt_f_of_s, 'all');
% Call Function
mp_cl_mt_xyz_of_s_out = ff_simu_stats(mt_f_of_s, mp_cl_mt_xyz_of_s);
xxx tb_outcomes: all stats xxx
OriginalVariableNames cl_mt_x_of_s cl_mt_y_of_s cl_mt_z_of_s
_______________________ ____________ ____________ ____________
{'mean' } 2.0763 1.9323 2.0668
{'sd' } 0.9071 5.2239 0.9042
{'coefofvar' } 0.43688 2.7034 0.43749
{'min' } 1 -10 1
{'max' } 4 9 4
{'pYis0' } 0 0 0
{'pYls0' } 0 0.20441 0
{'pYgr0' } 1 0.79559 1
{'pYisMINY' } 0.28039 0.10917 0.14247
{'pYisMAXY' } 0.044922 0.19422 0.044922
{'p1' } 1 -10 1
{'p10' } 1 -10 1
{'p25' } 1 1.1 1.1
{'p50' } 2 2 2
{'p75' } 3 5 2.5
{'p90' } 3 9 3.3
{'p99' } 4 9 4
{'fl_cov_cl_mt_x_of_s'} 0.82282 1.589 0.78646
{'fl_cor_cl_mt_x_of_s'} 1 0.33534 0.95887
{'fl_cov_cl_mt_y_of_s'} 1.589 27.289 1.8353
{'fl_cor_cl_mt_y_of_s'} 0.33534 1 0.38856
{'fl_cov_cl_mt_z_of_s'} 0.78646 1.8353 0.81758
{'fl_cor_cl_mt_z_of_s'} 0.95887 0.38856 1
{'fracByP1' } 0.13504 -0.56498 0.068934
{'fracByP10' } 0.13504 -0.56498 0.068934
{'fracByP25' } 0.13504 -0.53456 0.14234
{'fracByP50' } 0.42991 -0.39181 0.43856
{'fracByP75' } 0.91346 0.095425 0.60296
{'fracByP90' } 0.91346 1 0.91306
{'fracByP99' } 1 1 1 4.1.3 Test FF_SIMU_STATS Four States-Points Matrix Single Column Inputs
Same as before, but now inputs are single column, should have identical results:
% Array Inputs
mp_cl_ar_xyz_of_s = containers.Map('KeyType','char', 'ValueType','any');
mp_cl_mt_xyz_of_s('cl_mt_x_of_s') = {mt_x_of_s(:), zeros(1)};
mp_cl_mt_xyz_of_s('cl_mt_y_of_s') = {mt_y_of_s(:), zeros(1)};
mp_cl_mt_xyz_of_s('cl_mt_z_of_s') = {mt_z_of_s(:), zeros(1)};
mp_cl_mt_xyz_of_s('ar_st_y_name') = ["cl_mt_x_of_s", "cl_mt_y_of_s", "cl_mt_z_of_s"];
% Call Function
mp_cl_mt_xyz_of_s_out = ff_simu_stats(mt_f_of_s(:), mp_cl_mt_xyz_of_s);
xxx tb_outcomes: all stats xxx
OriginalVariableNames cl_mt_x_of_s cl_mt_y_of_s cl_mt_z_of_s
_______________________ ____________ ____________ ____________
{'mean' } 2.0763 1.9323 2.0668
{'sd' } 0.9071 5.2239 0.9042
{'coefofvar' } 0.43688 2.7034 0.43749
{'min' } 1 -10 1
{'max' } 4 9 4
{'pYis0' } 0 0 0
{'pYls0' } 0 0.20441 0
{'pYgr0' } 1 0.79559 1
{'pYisMINY' } 0.28039 0.10917 0.14247
{'pYisMAXY' } 0.044922 0.19422 0.044922
{'p1' } 1 -10 1
{'p10' } 1 -10 1
{'p25' } 1 1.1 1.1
{'p50' } 2 2 2
{'p75' } 3 5 2.5
{'p90' } 3 9 3.3
{'p99' } 4 9 4
{'fl_cov_cl_mt_x_of_s'} 0.82282 1.589 0.78646
{'fl_cor_cl_mt_x_of_s'} 1 0.33534 0.95887
{'fl_cov_cl_mt_y_of_s'} 1.589 27.289 1.8353
{'fl_cor_cl_mt_y_of_s'} 0.33534 1 0.38856
{'fl_cov_cl_mt_z_of_s'} 0.78646 1.8353 0.81758
{'fl_cor_cl_mt_z_of_s'} 0.95887 0.38856 1
{'fracByP1' } 0.13504 -0.56498 0.068934
{'fracByP10' } 0.13504 -0.56498 0.068934
{'fracByP25' } 0.13504 -0.53456 0.14234
{'fracByP50' } 0.42991 -0.39181 0.43856
{'fracByP75' } 0.91346 0.095425 0.60296
{'fracByP90' } 0.91346 1 0.91306
{'fracByP99' } 1 1 1 4.1.4 Test FF_SIMU_STATS Print Many Details
The Same As before, but now control which percentiles and other details to display.
% Array Inputs
mp_cl_ar_xyz_of_s = containers.Map('KeyType','char', 'ValueType','any');
mp_cl_ar_xyz_of_s('cl_ar_x_of_s') = {mt_x_of_s(:), zeros(1)};
mp_cl_ar_xyz_of_s('cl_ar_z_of_s') = {mt_z_of_s(:), zeros(1)};
mp_cl_ar_xyz_of_s('ar_st_y_name') = ["cl_ar_x_of_s", "cl_ar_z_of_s"];
% controls
mp_support = containers.Map('KeyType','char', 'ValueType','any');
mp_support('bl_display_detail') = false;
mp_support('bl_display_final') = true;
mp_support('bl_display_drvm2outcomes') = false;
mp_support('ar_fl_percentiles') = [25 50 75];
mp_support('bl_display_drvstats') = true;
mp_support('bl_display_drvm2covcor') = false;
% Call Function
mp_cl_mt_xyz_of_s_out = ff_simu_stats(mt_f_of_s(:), mp_cl_ar_xyz_of_s, mp_support);
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Summary Statistics for: cl_ar_x_of_s
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fl_choice_mean
2.0763
fl_choice_sd
0.9071
fl_choice_coefofvar
0.4369
fl_choice_prob_zero
0
fl_choice_prob_below_zero
0
fl_choice_prob_above_zero
1
fl_choice_prob_max
0.0449
tb_disc_cumu
cl_ar_x_of_sDiscreteVal cl_ar_x_of_sDiscreteValProbMass CDF cumsumFrac
_______________________ _______________________________ ______ __________
1 0.28039 28.039 0.13504
1.5 0.13561 41.6 0.23301
2 0.20441 62.041 0.42991
3 0.33466 95.508 0.91346
4 0.044922 100 1
cl_ar_x_of_sDiscreteVal cl_ar_x_of_sDiscreteValProbMass CDF cumsumFrac
_______________________ _______________________________ ______ __________
1 0.28039 28.039 0.13504
1.5 0.13561 41.6 0.23301
2 0.20441 62.041 0.42991
3 0.33466 95.508 0.91346
4 0.044922 100 1
tb_prob_drv
percentiles cl_ar_x_of_sDiscreteValPercentileValues fracOfSumHeldBelowThisPercentile
___________ _______________________________________ ________________________________
25 1 0.13504
50 2 0.42991
75 3 0.91346
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Summary Statistics for: cl_ar_z_of_s
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fl_choice_mean
2.0668
fl_choice_sd
0.9042
fl_choice_coefofvar
0.4375
fl_choice_prob_zero
0
fl_choice_prob_below_zero
0
fl_choice_prob_above_zero
1
fl_choice_prob_max
0.0449
tb_disc_cumu
cl_ar_z_of_sDiscreteVal cl_ar_z_of_sDiscreteValProbMass CDF cumsumFrac
_______________________ _______________________________ ______ __________
1 0.14247 14.247 0.068934
1.1 0.13792 28.039 0.14234
1.5 0.13561 41.6 0.24076
2 0.20441 62.041 0.43856
2.3 0.056663 67.708 0.50162
2.5 0.083786 76.086 0.60296
3.3 0.19422 95.508 0.91306
4 0.044922 100 1
cl_ar_z_of_sDiscreteVal cl_ar_z_of_sDiscreteValProbMass CDF cumsumFrac
_______________________ _______________________________ ______ __________
1 0.14247 14.247 0.068934
1.1 0.13792 28.039 0.14234
1.5 0.13561 41.6 0.24076
2 0.20441 62.041 0.43856
2.3 0.056663 67.708 0.50162
2.5 0.083786 76.086 0.60296
3.3 0.19422 95.508 0.91306
4 0.044922 100 1
tb_prob_drv
percentiles cl_ar_z_of_sDiscreteValPercentileValues fracOfSumHeldBelowThisPercentile
___________ _______________________________________ ________________________________
25 1.1 0.14234
50 2 0.43856
75 2.5 0.60296
xxx tb_outcomes: all stats xxx
OriginalVariableNames cl_ar_x_of_s cl_ar_z_of_s
_______________________ ____________ ____________
{'mean' } 2.0763 2.0668
{'sd' } 0.9071 0.9042
{'coefofvar' } 0.43688 0.43749
{'min' } 1 1
{'max' } 4 4
{'pYis0' } 0 0
{'pYls0' } 0 0
{'pYgr0' } 1 1
{'pYisMINY' } 0.28039 0.14247
{'pYisMAXY' } 0.044922 0.044922
{'p25' } 1 1.1
{'p50' } 2 2
{'p75' } 3 2.5
{'fl_cov_cl_ar_x_of_s'} 0.82282 0.78646
{'fl_cor_cl_ar_x_of_s'} 1 0.95887
{'fl_cov_cl_ar_z_of_s'} 0.78646 0.81758
{'fl_cor_cl_ar_z_of_s'} 0.95887 1
{'fracByP25' } 0.13504 0.14234
{'fracByP50' } 0.42991 0.43856
{'fracByP75' } 0.91346 0.60296 4.2 FF_DISC_RAND_VAR_STATS Examples
Go back to fan’s MEconTools Toolbox (bookdown), Matlab Code Examples Repository (bookdown), or Math for Econ with Matlab Repository (bookdown).
Examples](https://fanwangecon.github.io/M4Econ/), or** Dynamic Asset This is the example vignette for function: ff_disc_rand_var_stats from the MEconTools Package. This function summarizes statistics of matrixes stored in a container map, as well as scalar, string, function and other values stored in container maps.
4.2.1 Test FF_DISC_RAND_VAR_STATS Defaults
Call the function with defaults.
ff_disc_rand_var_stats();
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Summary Statistics for: binom
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fl_choice_mean
-1.0000
fl_choice_sd
2.5100
fl_choice_coefofvar
-2.5100
fl_choice_prob_zero
0.1416
fl_choice_prob_below_zero
0.5888
fl_choice_prob_above_zero
0.2696
fl_choice_prob_max
2.0589e-16
tb_disc_cumu
binomDiscreteVal binomDiscreteValProbMass CDF cumsumFrac
________________ ________________________ _________ __________
-10 2.2539e-05 0.0022539 0.00022539
-9 0.00028979 0.031233 0.0028335
-8 0.0018008 0.21132 0.01724
-7 0.0072034 0.93166 0.067664
-6 0.020838 3.0155 0.19269
-5 0.04644 7.6595 0.42489
-4 0.082928 15.952 0.75661
-3 0.12185 28.138 1.1222
-2 0.15014 43.152 1.4224
-1 0.15729 58.881 1.5797
binomDiscreteVal binomDiscreteValProbMass CDF cumsumFrac
________________ ________________________ ___ __________
11 6.0392e-06 100 1
12 1.0588e-06 100 1
13 1.5784e-07 100 1
14 1.973e-08 100 1
15 2.0293e-09 100 1
16 1.6725e-10 100 1
17 1.0619e-11 100 1
18 4.8762e-13 100 1
19 1.4412e-14 100 1
20 2.0589e-16 100 1
tb_prob_drv
percentiles binomDiscreteValPercentileValues fracOfSumHeldBelowThisPercentile
___________ ________________________________ ________________________________
0.1 -8 0.01724
1 -6 0.19269
5 -5 0.42489
10 -4 0.75661
15 -4 0.75661
20 -3 1.1222
25 -3 1.1222
35 -2 1.4224
50 -1 1.5797
65 0 1.5797
75 1 1.4694
80 1 1.4694
85 2 1.3197
90 2 1.3197
95 3 1.1865
99 5 1.0412
99.9 7 1.0052 4.2.2 Test FF_DISC_RAND_VAR_STATS 0 and 1 Random Variable
The simplest discrete random variable has two values, zero or one. The probability of zero is 30 percent, and 70 percent is the probability of one.
% Parameters
% 1. specify the random variable
st_var_name = 'bernoulli';
ar_choice_unique_sorted = [0, 1];
ar_choice_prob = [0.3, 0.7];
% 2. percentiles of interest
ar_fl_percentiles = [0.1 5 25 50 75 95 99.9];
% 3. print resutls
bl_display_drvstats = true;
% Call Function
[ds_stats_map] = ff_disc_rand_var_stats(st_var_name, ...
ar_choice_unique_sorted, ar_choice_prob, ...
ar_fl_percentiles, bl_display_drvstats);
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Summary Statistics for: bernoulli
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fl_choice_mean
0.7000
fl_choice_sd
0.4583
fl_choice_coefofvar
0.6547
fl_choice_prob_zero
0.3000
fl_choice_prob_below_zero
0
fl_choice_prob_above_zero
0.7000
fl_choice_prob_max
0.7000
tb_disc_cumu
bernoulliDiscreteVal bernoulliDiscreteValProbMass CDF cumsumFrac
____________________ ____________________________ ___ __________
0 0.3 30 0
1 0.7 100 1
bernoulliDiscreteVal bernoulliDiscreteValProbMass CDF cumsumFrac
____________________ ____________________________ ___ __________
0 0.3 30 0
1 0.7 100 1
tb_prob_drv
percentiles bernoulliDiscreteValPercentileValues fracOfSumHeldBelowThisPercentile
___________ ____________________________________ ________________________________
0.1 0 0
5 0 0
25 0 0
50 1 1
75 1 1
95 1 1
99.9 1 1 4.2.3 Test FF_DISC_RAND_VAR_STATS with Poisson
Poisson random variable, with mean equals to ten, summarize over umsymmetric percentiles. Note that the poisson random variable has no upper bound.
% Parameters
% 1. specify the random variable
st_var_name = 'poisson';
mu = 10;
ar_choice_unique_sorted = 0:1:50;
ar_choice_prob = poisspdf(ar_choice_unique_sorted, mu);
% 2. percentiles of interest, unsymmetric
ar_fl_percentiles = [0.1 5 10 25 50 90 95 99 99.9 99.99 99.999 99.9999];
% 3. print resutls
bl_display_drvstats = true;
% Call Function
[ds_stats_map] = ff_disc_rand_var_stats(st_var_name, ...
ar_choice_unique_sorted, ar_choice_prob, ...
ar_fl_percentiles, bl_display_drvstats);
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Summary Statistics for: poisson
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fl_choice_mean
10
fl_choice_sd
3.1623
fl_choice_coefofvar
0.3162
fl_choice_prob_zero
4.5400e-05
fl_choice_prob_below_zero
0
fl_choice_prob_above_zero
1.0000
fl_choice_prob_max
1.4927e-19
tb_disc_cumu
poissonDiscreteVal poissonDiscreteValProbMass CDF cumsumFrac
__________________ __________________________ _______ __________
0 4.54e-05 0.00454 0
1 0.000454 0.04994 4.54e-05
2 0.00227 0.27694 0.0004994
3 0.0075667 1.0336 0.0027694
4 0.018917 2.9253 0.010336
5 0.037833 6.7086 0.029253
6 0.063055 13.014 0.067086
7 0.090079 22.022 0.13014
8 0.1126 33.282 0.22022
9 0.12511 45.793 0.33282
poissonDiscreteVal poissonDiscreteValProbMass CDF cumsumFrac
__________________ __________________________ ___ __________
41 1.3571e-13 100 1
42 3.2313e-14 100 1
43 7.5146e-15 100 1
44 1.7079e-15 100 1
45 3.7953e-16 100 1
46 8.2506e-17 100 1
47 1.7554e-17 100 1
48 3.6572e-18 100 1
49 7.4636e-19 100 1
50 1.4927e-19 100 1
tb_prob_drv
percentiles poissonDiscreteValPercentileValues fracOfSumHeldBelowThisPercentile
___________ __________________________________ ________________________________
0.1 2 0.0004994
5 5 0.029253
10 6 0.067086
25 8 0.22022
50 10 0.45793
90 14 0.86446
95 15 0.91654
99 18 0.98572
99.9 21 0.99841
99.99 24 0.99988
99.999 26 0.99998
100 28 1
% Print out full Stored Matrix
% Note that the outputs are single row arrays.
ff_container_map_display(ds_stats_map, 100, 100)
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CONTAINER NAME: ds_stats_map ND Array (Matrix etc)
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i idx ndim numel rowN colN sum mean std coefvari min max
_ ___ ____ _____ ____ ____ ______ _______ ______ ________ _________ ___
ar_choice_perc_fracheld 1 1 2 12 1 12 7.54 0.62833 0.435 0.69231 0.0004994 1
ar_choice_percentiles 2 2 2 12 1 12 177 14.75 8.7399 0.59254 2 28
ar_fl_percentiles 3 3 2 12 1 12 773.99 64.499 42.887 0.66492 0.1 100
xxx TABLE:ar_choice_perc_fracheld xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12
_________ ________ ________ _______ _______ _______ _______ _______ _______ _______ _______ ___
r1 0.0004994 0.029253 0.067086 0.22022 0.45793 0.86446 0.91654 0.98572 0.99841 0.99988 0.99998 1
xxx TABLE:ar_choice_percentiles xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12
__ __ __ __ __ __ __ __ __ ___ ___ ___
r1 2 5 6 8 10 14 15 18 21 24 26 28
xxx TABLE:ar_fl_percentiles xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12
___ __ __ __ __ __ __ __ ____ _____ ______ ___
r1 0.1 5 10 25 50 90 95 99 99.9 99.99 99.999 100
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CONTAINER NAME: ds_stats_map Scalars
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i idx value
__ ___ __________
fl_choice_coefofvar 1 4 0.31623
fl_choice_max 2 5 50
fl_choice_mean 3 6 10
fl_choice_min 4 7 0
fl_choice_prob_above_zero 5 8 0.99995
fl_choice_prob_below_zero 6 9 0
fl_choice_prob_max 7 10 1.4927e-19
fl_choice_prob_min 8 11 4.54e-05
fl_choice_prob_zero 9 12 4.54e-05
fl_choice_sd 10 13 3.16234.3 FF_DISC_RAND_VAR_MASS2OUTCOMES Examples
Go back to fan’s MEconTools Toolbox (bookdown), Matlab Code Examples Repository (bookdown), or Math for Econ with Matlab Repository (bookdown).
Examples](https://fanwangecon.github.io/M4Econ/), or** Dynamic Asset This is the example vignette for function: ff_disc_rand_var_mass2outcomes from the MEconTools Package. This function generates sorted discrete random variable from state-space joint distribution.
4.3.1 Test FF_DISC_RAND_VAR_MASS2OUTCOMES Defaults
Call the function with defaults.
ff_disc_rand_var_mass2outcomes();
INPUT f(a,z): mt_dist_bystates
0.0289 0.0465 0.0228 0.0036 0.0001
0.0241 0.0930 0.0857 0.0241 0.0015
0.0080 0.0744 0.1285 0.0643 0.0074
0.0013 0.0297 0.0964 0.0857 0.0186
0.0001 0.0059 0.0361 0.0571 0.0232
0.0000 0.0005 0.0054 0.0152 0.0116
INPUT y(a,z): mt_choice_bystates
-5 -4 -5 -4 -4
-3 -2 -3 -2 -3
-1 -1 -1 0 0
1 1 2 3 1
4 3 3 4 3
5 6 5 6 6
OUTPUT f(y): ar_choice_prob_byY
0.0518
0.0502
0.1113
0.1171
0.2109
0.0717
0.0497
0.0964
0.1510
0.0572
0.0054
0.0273
OUTPUT f(y,z): mt_choice_prob_byYZ
0.0289 0 0.0228 0 0
0 0.0465 0 0.0036 0.0001
0.0241 0 0.0857 0 0.0015
0 0.0930 0 0.0241 0
0.0080 0.0744 0.1285 0 0
0 0 0 0.0643 0.0074
0.0013 0.0297 0 0 0.0186
0 0 0.0964 0 0
0 0.0059 0.0361 0.0857 0.0232
0.0001 0 0 0.0571 0
0.0000 0 0.0054 0 0
0 0.0005 0 0.0152 0.0116
OUTPUT f(y,a): mt_choice_prob_byYA
0.0518 0 0 0 0 0
0.0502 0 0 0 0 0
0 0.1113 0 0 0 0
0 0.1171 0 0 0 0
0 0 0.2109 0 0 0
0 0 0.0717 0 0 0
0 0 0 0.0497 0 0
0 0 0 0.0964 0 0
0 0 0 0.0857 0.0653 0
0 0 0 0 0.0572 0
0 0 0 0 0 0.0054
0 0 0 0 0 0.0273
OUTPUT f(y) and y in table: tb_choice_drv_cur_byY
binomtestOutcomes probMassFunction
_________________ ________________
-5 0.051764
-4 0.050217
-3 0.11126
-2 0.11706
-1 0.21092
0 0.071696
1 0.049682
2 0.096388
3 0.15102
4 0.057231
5 0.0054256
6 0.027329 4.3.2 Test FF_DISC_RAND_VAR_MASS2OUTCOMES Four States-Points
Over some (a,z) states that is 2 by 2, matrix or vectorized inputs identical results.
% Set Parameters
st_y_name = 'consumption';
% consumption matrix: c(a,z)
mt_c_of_s = [1,2;3,1];
% stationary mass over assets adn shocks: f(a,z)
mt_f_of_s = rand(size(mt_c_of_s));
mt_f_of_s = mt_f_of_s/sum(mt_f_of_s, 'all');
% Call Function
[ar_f_of_y, ar_y_unique_sorted] = ...
ff_disc_rand_var_mass2outcomes(st_y_name, mt_c_of_s, mt_f_of_s);
% print
disp([ar_f_of_y ar_y_unique_sorted]);
0.4039 1.0000
0.2971 2.0000
0.2990 3.0000Same as before, but now inputs are single column:
% Call Function
[ar_f_of_y, ar_y_unique_sorted] = ...
ff_disc_rand_var_mass2outcomes(st_y_name, mt_c_of_s(:), mt_f_of_s);
disp([ar_f_of_y ar_y_unique_sorted]);
0.4039 1.0000
0.2971 2.0000
0.2990 3.00004.3.3 Test FF_DISC_RAND_VAR_MASS2OUTCOMES Conditional Mass Outputs
Same inputs as before, but now, also output additional conditional statistis, f(y, a), where a is the row state variable for f(a,z). For conditional statistics, must provide matrix based inputs.
% Set Parameters
st_y_name = 'consumption';
% consumption matrix: c(a,z)
mt_c_of_s = [1,2,0.5;
3,1,2.0];
% stationary mass over assets adn shocks: f(a,z)
mt_f_of_s = rand(size(mt_c_of_s));
mt_f_of_s = mt_f_of_s/sum(mt_f_of_s, 'all');
% Call Function
[ar_f_of_y, ar_y_unique_sorted, mt_f_of_y_srow, mt_f_of_y_scol] = ...
ff_disc_rand_var_mass2outcomes(st_y_name, mt_c_of_s, mt_f_of_s);
% print
disp([ar_f_of_y ar_y_unique_sorted]);
0.2695 0.5000
0.3765 1.0000
0.2649 2.0000
0.0891 3.0000
disp(mt_f_of_y_srow);
0.2695 0
0.1215 0.2550
0.1217 0.1432
0 0.0891
disp(mt_f_of_y_scol);
0 0 0.2695
0.1215 0.2550 0
0 0.1217 0.1432
0.0891 0 04.4 FF_DISC_RAND_VAR_MASS2COVCOR Examples
Go back to fan’s MEconTools Toolbox (bookdown), Matlab Code Examples Repository (bookdown), or Math for Econ with Matlab Repository (bookdown).
Examples](https://fanwangecon.github.io/M4Econ/), or** Dynamic Asset This is the example vignette for function: ff_disc_rand_var_mass2covcor from the MEconTools Package. This function calculates covariance and correlation based for two discrete random variables.
4.4.1 Test FF_DISC_RAND_VAR_MASS2COVCOR Defaults
Call the function with defaults.
ff_disc_rand_var_mass2covcor();
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
CONTAINER NAME: covvar_input_map ND Array (Matrix etc)
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
i idx ndim numel rowN colN sum mean std coefvari min max
_ ___ ____ _____ ____ ____ ______ ________ ________ ________ __________ _______
mt_f_of_s 1 5 2 30 6 5 1 0.033333 0.035743 1.0723 3.7187e-06 0.12852
mt_x_of_s 2 6 2 30 6 5 25 0.83333 5.3051 6.3661 -7 9
mt_y_of_s 3 7 2 30 6 5 249.78 8.3259 7.1913 0.86373 -6.3772 21.786
xxx TABLE:mt_f_of_s xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4 c5
__________ __________ _________ _________ _________
r1 0.028917 0.046484 0.022848 0.0036146 0.000119
r2 0.024097 0.092967 0.085679 0.024097 0.0014875
r3 0.0080324 0.074374 0.12852 0.064259 0.0074374
r4 0.0013387 0.02975 0.096388 0.085679 0.018593
r5 0.00011156 0.0059499 0.036146 0.057119 0.023242
r6 3.7187e-06 0.00047599 0.0054218 0.015232 0.011621
xxx TABLE:mt_x_of_s xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4 c5
__ __ __ __ __
r1 -7 -6 -7 -6 -6
r2 -5 -3 -5 -3 -4
r3 -2 -1 -1 0 -1
r4 2 2 3 4 2
r5 6 5 5 6 5
r6 8 9 7 9 9
xxx TABLE:mt_y_of_s xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4 c5
______ ________ ______ _______ _______
r1 13.231 21.786 18.136 19.35 13.901
r2 9.946 16.887 9.6914 15.71 8.6906
r3 16.255 6.2166 13.799 5.2138 11.641
r4 12.628 2.7525 6.5321 0.27238 13.357
r5 5.8844 4.0352 6.05 0.14102 0.50318
r6 3.5617 -0.72091 5.1855 -6.3772 -4.4805
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
CONTAINER NAME: covvar_input_map Scalars
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
i idx value
_ ___ ________
fl_x_mean 1 1 -0.11081
fl_x_sd 2 2 4.1239
fl_y_mean 3 3 8.8423
fl_y_sd 4 4 6.5845
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
CONTAINER NAME: covvar_output_map ND Array (Matrix etc)
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
i idx ndim numel rowN colN sum mean std coefvari min max
_ ___ ____ _____ ____ ____ _______ ________ ______ ________ _______ _______
mt_cov_component_weighted 1 1 2 30 6 5 -22.084 -0.73612 1.0404 -1.4134 -3.5432 0.17717
mt_x_devi_from_mean 2 2 2 30 6 5 28.324 0.94415 5.3051 5.6189 -6.8892 9.1108
mt_x_y_multiply 3 3 2 30 6 5 -939.63 -31.321 36.564 -1.1674 -138.66 9.5287
mt_y_devi_from_mean 4 4 2 30 6 5 -15.493 -0.51644 7.1913 -13.925 -15.22 12.943
xxx TABLE:mt_cov_component_weighted xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4 c5
___________ _________ ________ _________ __________
r1 -0.87434 -3.5432 -1.4628 -0.22368 -0.0035451
r2 -0.13003 -2.1607 -0.35565 -0.47814 0.00087767
r3 -0.11248 0.17365 -0.56642 -0.025838 -0.018507
r4 0.010697 -0.38241 -0.69273 -3.0184 0.17717
r5 -0.0020165 -0.14618 -0.51584 -3.0371 -0.99056
r6 -0.00015927 -0.041473 -0.14098 -2.1121 -1.4106
xxx TABLE:mt_x_devi_from_mean xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4 c5
_______ ________ ________ _______ ________
r1 -6.8892 -5.8892 -6.8892 -5.8892 -5.8892
r2 -4.8892 -2.8892 -4.8892 -2.8892 -3.8892
r3 -1.8892 -0.88919 -0.88919 0.11081 -0.88919
r4 2.1108 2.1108 3.1108 4.1108 2.1108
r5 6.1108 5.1108 5.1108 6.1108 5.1108
r6 8.1108 9.1108 7.1108 9.1108 9.1108
xxx TABLE:mt_x_y_multiply xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4 c5
_______ _______ _______ ________ _______
r1 -30.237 -76.225 -64.023 -61.882 -29.792
r2 -5.396 -23.242 -4.151 -19.842 0.59004
r3 -14.003 2.3348 -4.4073 -0.40209 -2.4884
r4 7.9905 -12.854 -7.1868 -35.23 9.5287
r5 -18.075 -24.568 -14.271 -53.172 -42.62
r6 -42.83 -87.129 -26.003 -138.66 -121.38
xxx TABLE:mt_y_devi_from_mean xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4 c5
_______ _______ _______ _______ ________
r1 4.389 12.943 9.2933 10.508 5.0587
r2 1.1037 8.0444 0.84902 6.8677 -0.15171
r3 7.4123 -2.6258 4.9566 -3.6286 2.7985
r4 3.7855 -6.0898 -2.3103 -8.57 4.5142
r5 -2.9579 -4.8071 -2.7924 -8.7013 -8.3392
r6 -5.2806 -9.5633 -3.6568 -15.22 -13.323
fl_cov
-22.0835
fl_cor
-0.81334.4.2 Test FF_DISC_RAND_VAR_MASS2COVCOR Four States-Points
Over some (a,z) states that is 2 by 2, c matrix, and y matrix, find correlation. Positively related.
% Set Parameters
mt_c_of_s = [1,2;3,1];
mt_y_of_s = [2,10;5,1.1];
rng(123);
mt_f_of_s = rand(size(mt_c_of_s));
mt_f_of_s = mt_f_of_s/sum(mt_f_of_s, 'all');
bl_display_drvm2covcor = false;
% Call Function
[fl_cov_xy, fl_cor_xy] = ff_disc_rand_var_mass2covcor(...
mt_c_of_s, mt_y_of_s, mt_f_of_s, bl_display_drvm2covcor);
display(['cov=' num2str(fl_cov_xy) ',cor=', num2str(fl_cor_xy)]);
cov=1.4446,cor=0.65723Same as before, but now inputs are single column:
% Call Function
[fl_cov_xy, fl_cor_xy] = ff_disc_rand_var_mass2covcor(...
mt_c_of_s(:), mt_y_of_s(:), mt_f_of_s(:), bl_display_drvm2covcor);
display(['cov=' num2str(fl_cov_xy) ',cor=', num2str(fl_cor_xy)]);
cov=1.4446,cor=0.657234.4.3 Test FF_DISC_RAND_VAR_MASS2COVCOR Two Random Vectors
Generate two random vectors, with random or even mass, correlation should be zero:
% Set Parameters
rng(4567);
mt_c_of_s = rand([20,1])*100;
mt_y_of_s = rand([20,1])*100;
mt_f_of_s = rand(size(mt_c_of_s));
mt_f_of_s = mt_f_of_s/sum(mt_f_of_s, 'all');
bl_display_drvm2covcor = false;
% Call Function
[fl_cov_xy, fl_cor_xy] = ff_disc_rand_var_mass2covcor(...
mt_c_of_s, mt_y_of_s, mt_f_of_s, bl_display_drvm2covcor);
display(['cov=' num2str(fl_cov_xy) ',cor=', num2str(fl_cor_xy)]);
cov=-57.6533,cor=-0.0620234.4.4 Test FF_DISC_RAND_VAR_MASS2COVCOR Provide Mean and SD
Same as above, but now provide means and sd for x andy directly. The results are the same as when mean and sd are calculated inside the function.
% Set Parameters
rng(4567);
mt_c_of_s = rand([20,1])*100;
mt_y_of_s = rand([20,1])*100;
mt_f_of_s = rand(size(mt_c_of_s));
mt_f_of_s = mt_f_of_s/sum(mt_f_of_s, 'all');
fl_c_mean = sum(mt_f_of_s.*mt_c_of_s);
fl_c_sd = sqrt(sum(mt_f_of_s.*(mt_c_of_s-fl_c_mean).^2));
fl_y_mean = sum(mt_f_of_s.*mt_y_of_s);
fl_y_sd = sqrt(sum(mt_f_of_s.*(mt_y_of_s-fl_y_mean).^2));
bl_display_drvm2covcor = false;
% Call Function
[fl_cov_xy, fl_cor_xy] = ff_disc_rand_var_mass2covcor(...
mt_c_of_s, mt_y_of_s, mt_f_of_s, ...
fl_c_mean, fl_c_sd, ...
fl_y_mean, fl_y_sd, bl_display_drvm2covcor);
display(['cov=' num2str(fl_cov_xy) ',cor=', num2str(fl_cor_xy)]);
cov=-57.6533,cor=-0.062023