% ch8example7prog2.m
clear;
n1=5; n2=4; % F分布的參數(shù)
N=1000;     % 隨機數(shù)樣本數(shù)量
x=frnd(n1,n2,N,1);  % 隨機數(shù)樣本產(chǎn)生
%x=normrnd(5,1,N,1);
a=0;  b=5;  % 樣本值域區(qū)間計算
n=20;               % 分組區(qū)間數(shù)
Delta=(b-a)/n;      % 分組間隔
[m,xout]=hist(x,[a:Delta:b]+Delta/2);    % 計算直方圖數(shù)據(jù)
% 統(tǒng)計分隔點為： -inf, a, a+Delta, a+2*Delta, ..., a+(n-1)Delta, b, +inf
%xout=[a:Delta:b-Delta];  % 分組間隔向量

% pdf=m./(N*Delta);                % 計算統(tǒng)計頻率密度
% %bar(xout,pdf);hold on;           % 作出頻率密度直方圖
% % h = findobj(gca,'Type','patch'); % 修改直方圖樣式
% % set(h,'FaceColor',[0.7,0.7,0.7],'EdgeColor','k');
% X=0:0.01:10; % 計算并畫出F分布的理論概率密度函數(shù)曲線
% Y = fpdf(X,n1,n2); 
% plot(X,Y,'k-');axis([0 10 0 1]); hold on; 

% p(1)=fcdf(a,n1,n2);
% p(m+2)=1-fcdf(b,n1,n2);


for i=2:n
    p(i) = fcdf(a+i*Delta,n1,n2)-fcdf(a+(i-1)*Delta,n1,n2);
end
p(1)=fcdf(a+Delta,n1,n2);
p(n+1)=1-fcdf(a+n*Delta,n1,n2);
 plot(xout,p*N,'-o');hold on;
 plot(xout,m,'*');
% 
chi2=sum((m-N*p).^2./(N*p))
alpha=0.01;
r=0;
chi2_alpha=chi2inv(1-alpha,n-r-1)

%-----
% mu=mean(x);
% sigma=std(x,1);
% r=2;
% for i=2:n
%     p(i) = normcdf(a+i*Delta,mu,sigma)-normcdf(a+(i-1)*Delta,mu,sigma);
% end
% p(1)=normcdf(a+Delta,mu,sigma);
% p(n+1)=1-normcdf(a+n*Delta,mu,sigma);
% chi2=sum((m-N*p).^2./(N*p))
% alpha=0.05;
% r=0;
% chi2_alpha=chi2inv(1-alpha,n-r-1)
%  plot(xout,p/Delta,'o');hold on;
%  plot(xout,pdf,'*');