How to determine error between two distributions
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Hello, I have the following code for comparing real and estimated distributions. The histogram represents the real while the curve is the estimated. How can I get the error (either the RMSE or R-squared) between the two curves. Any slight lead would be appreciated. As a far as am concerned its not possible to simply compare A and values obtained from wblpdf(sort(A),Overal_parameters(1),Overal_parameters(2)) since they're very different data types with different units. I suspect somehow we have to get probability distribution of the real data and compare it with the distribution obtain from wblpdf().
rng default
A=rnd(6000,1)
[Overal_parameters]= wblfit(A);
figure()
histogram(A,'Normalization','probability')
hold on
plot(sort(A),wblpdf(sort(A),Overal_parameters(1),Overal_parameters(2)))
legend('Observed Samples','Estimated Distribution')
xlabel('Mean wind speed (m/s)')
ylabel('Annual probabilty density')
hold off
1 commentaire
Paul
le 13 Juin 2023
The graphical comparison should use pdf normalization of the histogram.
Original code, but use use an actual Weibull distribution for the data
rng default
%A=rnd(6000,1);
A = wblrnd(4,3,6000,1);
[Overal_parameters]= wblfit(A)
figure()
histogram(A,'Normalization','probability')
hold on
plot(sort(A),wblpdf(sort(A),Overal_parameters(1),Overal_parameters(2)))
legend('Observed Samples','Estimated Distribution')
xlabel('Mean wind speed (m/s)')
ylabel('Annual probabilty density')
hold off
Use pdf normalization to compare to the estimated pdf
figure()
histogram(A,'Normalization','pdf')
hold on
plot(sort(A),wblpdf(sort(A),Overal_parameters(1),Overal_parameters(2)))
legend('Observed Samples','Estimated Distribution')
xlabel('Mean wind speed (m/s)')
ylabel('Annual probabilty density')
hold off
I'm not sure what the goal is from here, but at least now the graphs comparable.
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