I want to determine if the data(tmin) are Gaussian distributed or not by using Montecarlo simulation with skewness.

nn=143;

for n=1:1000;

load('ERA_Livneh_Birmingham.mat')

ss(n)=std(tmin);

m(n)=mean(tmin);

med(n)=median(tmin);

nu(n)=numel(tmin)

skew_FP(n) = sum((r-m(n)).^3)/(length(n)-1)/ss(n).^3

end

hist(skew_FP())

xlabel('Skew_FP()')

ylabel('Frequency')

In this case, what do I have to change for doing montecarlo simulation by using skewness??

[John D'Errico]

How will that determine if your data happen to follow a normal distribution?

[Chris]

I will see if skewness distribution is similar to zero or not

Answer 1

[Ayush]

Hey Chris,

I understand that you want to know the changes required in your code for doing Montecarlo simulation using skewness.

If you intend to perform a "Monte Carlo simulation" to assess the uncertainty of the skewness calculation, you will need to introduce random variations in the data or model parameters. This could involve generating random samples or perturbing the existing data in a meaningful way to simulate different scenarios. I have provided a sample code below for the same:

nn = 143;
skewness_MC = zeros(1, nn);
for n = 1:nn
    load('ERA_Livneh_Birmingham.mat')
    
    % Introduce random variations or perturbations to the data
    perturbed_tmin = tmin + randn(size(tmin)); % Example: Adding Gaussian noise
    
    ss(n) = std(perturbed_tmin);
    m(n) = mean(perturbed_tmin);
    med(n) = median(perturbed_tmin);
    nu(n) = numel(perturbed_tmin);
    skewness_MC(n) = sum((perturbed_tmin - m(n)).^3) / (length(perturbed_tmin) - 1) / ss(n).^3;
end
hist(skewness_MC)
xlabel('Skewness_MC')
ylabel('Frequency')

Hope this helps!