Go to the MLX, M, PDF, or HTML version of this file. 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.
Call the function with defaults.
ff_disc_rand_var_mass2covcor();
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CONTAINER NAME: covvar_input_map ND Array (Matrix etc)
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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
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CONTAINER NAME: covvar_input_map Scalars
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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
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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
-0.8133Over 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=0.65723Generate 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=-0.062023Same 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