N=100;    % 數(shù)據(jù)長(zhǎng)度
tht=10;  % 參數(shù)thita
x=exprnd(tht,1,N);   % 服從指數(shù)分布的數(shù)據(jù)
x1=sort(x);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 累積理論分布F(x)
tht0=mean(x);    % 估計(jì)理論參數(shù)值
for i=1:N-1
    expthcdf(i)=expcdf(x1(i),tht0);
end
expthcdf(N)=1;


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% 累積經(jīng)驗(yàn)分布函數(shù)S(x)
y=ones(1,N);  % 樣本出現(xiàn)次數(shù)初始化
k=0;          % 自適應(yīng)步長(zhǎng)初始化
for i=1:(1+k):(N-k)  % 自適應(yīng)調(diào)整步長(zhǎng)
    k=0;             % 循環(huán)一次后，步長(zhǎng)初始化
    for j=(i+1):N
        if x1(i)==x1(j)
            k=k+1;   % 若數(shù)據(jù)相等，則步長(zhǎng)加1
            for n=i:(i+k)   % 共有k+1個(gè)數(shù)據(jù)相等，都等于y(i)
                y(n)=1+k;   % 樣本出現(xiàn)次數(shù)。。。
            end
        end
    end
end

% 樣本出現(xiàn)次數(shù)數(shù)據(jù)處理
% 將重復(fù)的數(shù)據(jù)置零
t=1;
for i=1:t:(N-t+1)
    if y(i)>1
        t=y(i);
        for m=i+1:i+t-1
            y(m)=0;  % 次數(shù)相同的數(shù)據(jù)除第一項(xiàng)外均置零
        end
    end
end

% 樣本密度函數(shù)
for n=1:N
    pdf(n)=y(n)/N;  %處理后的樣本密度函數(shù)，并不為真實(shí)的密度函數(shù)
end

% 樣本分布函數(shù)
excdf(1)=pdf(1);
for n=2:N-1
    excdf(n)=excdf(n-1)+pdf(n);  % 樣本經(jīng)驗(yàn)分布函數(shù)S(x)
end
excdf(N)=1;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% K-S檢驗(yàn)
for i=1:N
    ks(i)=expthcdf(i)-excdf(i);
end
 expD=max(abs(ks));
 if expD<0.226
     disp('樣本數(shù)據(jù)服從指數(shù)分布。')
     subplot(2,2,3),plot(x1,excdf)      % 假設(shè)檢驗(yàn)經(jīng)驗(yàn)分布圖
             title('樣本擬合經(jīng)驗(yàn)分布S(x)')
             grid on
             subplot(2,2,4),plot(x1,expthcdf)  % 樣本理論分布圖
             title('假設(shè)檢驗(yàn)理論分布圖F(x)');
             grid on
 else
     disp('樣本數(shù)據(jù)不服從指數(shù)分布。')
 end
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % 畫圖
 % 圖1為樣本數(shù)據(jù)直方圖
 % 圖2為樣本數(shù)據(jù)數(shù)值圖
 % 圖3為假設(shè)檢驗(yàn)理論分布圖
 % 圖4為樣本數(shù)據(jù)的擬合分布圖
 subplot(2,2,1),hist(x)
 title('樣本數(shù)據(jù)直方圖');
  grid on
 subplot(2,2,2),stem(x)
 title('樣本數(shù)據(jù)數(shù)值圖');
 grid on
% THE END ! 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%