Distributions.m

clc, clear, close all
data = readtable('data/XrouterT.csv');
distros = ["Normal", "Lognormal", "GeneralizedExtremeValue", "Burr", "Stable"];%, "tLocationScale"];
n_params = [2, 2, 3, 3, 4];
n_distros = length(distros);
n_hops = 6;
counter = 0;
gaps = [0.090, 0.04];
xlabels = '\Delta (s)';
for i=1:n_hops
    figure;

    counter = 0;
    X = table2array(data(:, i));
    X = X(1:2000);
    distro_c = 0;
    for distro_s = distros
        distro_c = distro_c + 1;
        counter = counter + 1;
        distro = char(distro_s);
        %% Fit a una alpha-stable
        pd = fitdist(X, distro);
        
        %% Histograma vs PDF
        x_values = linspace(min(X), max(X), 1000);
        y = pdf(pd,x_values);
        sp = subtightplot(n_distros, 3, counter, gaps);

        
        plot(x_values,y, 'LineWidth',3)
        hold on;
        histogram(X, 20, 'Normalization', 'pdf')
        title(sprintf('Histograma y PDF de %s (Salto %d)', distro, i))
        set(sp,'FontSize',12);
        legend('PDF', 'Histograma')
        ylabel('f(x)')
        xlabel(xlabels)
        %set(gca, 'XScale', 'log')

        %% ECDF vs CDF
        counter = counter + 1;
        sp = subtightplot(n_distros, 3, counter, gaps);
        x = x_values;
        cdf_x = cdf(pd,x);
        plot(x,cdf_x,'m')
        hold on;
        cdfplot(X)
        title(sprintf('ECDF y CDF de %s (Salto %d)', distro, i))
        set(gca, 'XScale', 'log')
        set(sp,'FontSize',11);
        legend('CDF', 'ECDF')
        xlabel(xlabels)
        %% QQ plot
        counter = counter + 1;
        sp = subtightplot(n_distros, 3, counter, gaps);
        QQ = X(randperm(length(X), 100));
        QQ = X;
        qq_x = linspace(0.0001, 0.9999, length(QQ));
        qq_y = icdf(pd, qq_x);
        qq_z = sort(QQ);
        mdl = fitlm((qq_z),(qq_y));
        qqplot(QQ, pd)
        set(gca, 'XScale', 'log')
        set(gca, 'YScale', 'log')
        ylabel('Cuantiles de los datos')
        xlabel('Cuantiles de la distribución')
        k = n_params(distro_c);
        logL = sum(log(pdf(pd, X)));
        AIC = 2*k - 2*logL;
        BIC = log(length(X))*k-2*logL;
        set(sp,'FontSize', 9);
        title(sprintf('QQplot R2=%f R2adj=%f\n AIC=%f BIC=%f', mdl.Rsquared.Ordinary, mdl.Rsquared.Adjusted, AIC, BIC), 'FontSize', 12)
        %set(gca,'YTickLabelRotation',65)
    end
end