Testing lower Tail GPD Fit

Hi there,

I am trying to adjust the code below to test the fit of my lower tail instead of the upper tail (as the current code does). However, I have problems understanding the meaning of line 2 and 3 in the code. Specifically, I am unsure about the meaning of Q(1), P(1) and P(2) and thus how to change them to model the lower tail.

I would appreciate any hints!

Thanks in advance.

Carolin

%% Testing the GPD Fit _ Upper Tail

for i=1:nIndices

figure [P,Q] = boundary(tails{i}); % cumulative probabilities & quantiles at boundaries y = sort(residuals(residuals(:,i) > Q(2), i) + Q(2)); % sort exceedances plot(y, (cdf(tails{i}, y + Q(2)) - P(1))/P(2)) [F,x] = ecdf(y); % empirical CDF hold on stairs(x, F, 'r') grid on

legend('Fitted Generalized Pareto CDF','Empirical CDF','Location','SouthEast'); xlabel('Exceedance') ylabel('Probability') title('Upper Tail of Standardized Residuals') end