%Class for CO907, Fri, Week 1.
%__________________________________________
%Author: Jiarui Cao
%Date: 8 Nov 2013
%Purpose: Sheet1. Queation 1.7b


close all;
clear all;
clc;
clf;

%% We only do the simulation for one fixed n here. 
m=10000;
n=100;
%% Generate data.

%Data=rand(m,n); title('Uniform maximum');
%Data=exprnd(1,m,n); title('Exponential maximum');
Data=gprnd(0.1,1,1,[m,n]); title('Pareto maximum');

%% Take the max of each row.
maxData=zeros(m,1);
for i=1:m
    maxData(i)=max(Data(i,:));
end

hold on;

%% Plot
[f,xi]=ksdensity(maxData);
plot(xi,f,'om','Markersize',15);

paramhat=gevfit(maxData); %'gevfit' fits data by generalized extreme value distribution and returns 3 paramters stored in paramhat(1),paramhat(2) and paramhat(3).
y=gevpdf(xi,paramhat(1),paramhat(2),paramhat(3));%Use the parameters we fitted from data to generate the corresponding theoratical curve.
plot(xi,y,'k','linewidth',2);
hold off

xlabel('x');
ylabel('PDF');
legend('Data','Theory');