hist_for_avalanche_size

function slope_array = density_plot_avalanche_size(Aval, k_range)

tic;
%% DENSITY PLOT FOR AVALANCHE SIZE
% plotting actual density
subplot(2,2,1);
iii = 1;
maximum = 1;

avalanche_size_per_duration_k = []; 
for k = 1:k_range
    avalanche_k_portion2 = Aval(:,iii+2);
    avalanche_k_portion2 = sortrows(avalanche_k_portion2, 1);
    avalanche_k_portion = avalanche_k_portion2(avalanche_k_portion2 ~= 0);
    
    data = avalanche_k_portion(:);
    [nbins, ~] = histcounts(data, 'BinMethod', 'fd');
    normalized_pdf = nbins ./ sum(nbins);
    plot(1:length(nbins), normalized_pdf)
    hold on
    
    set(gca,'XScale','log');
    set(gca,'YScale','log');
    ax.YScale = 'log';
    ax.XScale = 'log';
    
    if length(nbins) > maximum
        maximum = max(length(nbins));
    end
    
    avalanche_size_per_duration_k(k, 1:length(normalized_pdf)) = normalized_pdf(1,:);
    iii = iii + 3;
end

%% reference lines with different slopes 
logx2 = log10(1:maximum);

y_vals_for_2 = 10.^[polyval([-2, -0.5],[logx2(1) logx2(end)])];
a = loglog([1 maximum], y_vals_for_2, '--', 'LineWidth', 1.5, 'Color', 'black');
hold on
uistack(a, 'top');
y_vals_for_1andhalf = 10.^[polyval([-1.5, -0.5],[logx2(1) logx2(end)])];
b = loglog([1 maximum], y_vals_for_1andhalf, '--', 'LineWidth', 1.5, 'Color', 'red');
hold on
uistack(b, 'top');
y_vals_for_1 = 10.^[polyval([-1, -0.5],[logx2(1) logx2(end)])];
c = loglog([1 maximum], y_vals_for_1, '--', 'LineWidth', 1.5, 'Color', 'green');
hold on
uistack(c, 'top');
y_vals_for_half = 10.^[polyval([-0.5, -0.5],[logx2(1) logx2(end)])];
d = loglog([1 maximum], y_vals_for_half, '--', 'LineWidth', 1.5, 'Color', 'blue');
hold on
uistack(d, 'top');

%% axis labels + scaling + plot adjustment
% labels
title('PDF for Avalanche Size (K = 1-10)', 'FontSize', 10);
xlabel('Avalanche Size Histogram Bin', 'FontSize', 10);
ylabel('Probability Density Function (PDF)', 'FontSize', 10);
axis square;
lgd = legend('k = 1', 'k = 2', 'k = 3', 'k = 4', 'k = 5', 'k = 6', 'k = 7', 'k = 8', 'k = 9', 'k = 10', '\alpha = 2', '\alpha = 1.5', '\alpha = 1', '\alpha = 0.5', ...
    'Location', 'northwest', 'Orientation', 'horizontal', 'NumColumns', 2);
lgd.FontSize = 6;
set(lgd, 'Position', [.282,.58,.1,.1]);

% axis scaling + limits
ylim([10.^-4 1]);
camroll(90);

%% log translating x and y + poly fitting to generate coefficients and line of best fit per k
iii = 1;
slope_array = [];

for k = 1:k_range
    logx = log10(1:10);
    logy = log10(avalanche_size_per_duration_k(k, 1:10));
    log_coefficients = polyfit(logx, logy, 1);
    
    slope_array(1, k) = abs(log_coefficients(1));
    
    iii = iii + 3;
end

fprintf('\nDone Generating Density Plot for Size\n')
toc;