%%Assignment 2.2

%%Ex.1
%%b
rng(123);
n=length(atlantic);
mles = est_gumbel(atlantic) %creating estimates of parameters from datafile
u = rand(n,1); % n uniform drawn between 0-1
x = -mles(1)*log(-log(u)) + mles(2); % using inverse transform method to
%create new "samples"

qqplot(x,atlantic)

%% c
B = 10000;
mles2 = zeros(B,2);
rng(123)
for i = 1:B  %parametric bootstrap
    u = rand(n,1);
    x = -mles(1)*log(-log(u)) + mles(2); %same code as in b)
    mles2(i,:) = est_gumbel(x); % creating new parameters from the new sample
end
mles2 = sort(mles2);
CI_beta = prctile(mles2(:,1),[2.5, 97.5]); %making percentile-confint
CI_mu = prctile(mles2(:,2),[2.5, 97.5]);


%% d
high = zeros(B); %where we want to store the highest wave that could be recorded
% during a 100 year
rng(123)
T = 3*14*100; % Times the wave occur "normally" under 100 years

high = -mles2(:,1)*log(-log(1-(1/T))) + mles(:,2); %u from b) & c) is switched to (1-(1/T))
high_ci = prctile(high, [2.5,97.5]);

%% f

for i = 1:B %making a non-parametric bootsample
    samp = randsample(atlantic,n,true); %taking a randomsample with replacement
    mles3(i,:) = est_gumbel(samp); %calculating and storing parameter each time
end
histogram(mles3(:,1))
histogram(mles3(:,2))