exindex.m

极值理论中各种函数及图像的程序。matlab实现。

function out=exindex(data,blocksize,opt)
%Estimates extremal index using blocks method
%
%    USAGE: out=exindex(data,blocksize,opt)
%
%     data: Data vector
%blocksize: Size of the blocks 
%      opt: Option for plotting.'t' or 'b' for plotting extremal index with respect to threshold
%           or number of blocks in which the threshold is exceeded. If not entered no plot is
%           generated.  
%
%      out: First column is K values (number of blocks in which a certain threshold is exceeded),
%           second column is the corresponding threshold value, 
%           third column is the corresponding extremal index estimates. 
warning off
if nargin>=2,
sorted=flipud(sort(data));
n=length(sorted);

r=blocksize;
k=round(n/r);
block_max=block(data,blocksize,'max');

block_max=flipud(sort(block_max(~isnan(block_max))));
un=unique(block_max);
un=un(1:end);
K=[];
for i=1:length(un),
    ki=un(i)==block_max;
    kif=find(ki);
    kif=kif(1);
    K(i)=kif-1;
end
N=[];
for i=1:length(un),
    ni=un(i)==sorted;
    nif=find(ni);
    nif=nif(1);
    N(i)=nif-1;
end
theta2=K./N;
theta=log(1-K/k)./(r*log(1-N/n));
out=[K',un,theta'];
out=out(1:end-1,:);
yrange=[min(theta) max(theta)];
index=K;
end
if nargin==3,
   if strcmp(opt,'t'),
      plot(un,theta)
      eval(['xlabel(''Threshold''),' ' ylabel([texlabel(''theta'') ' '''   (''' ' num2str(k) ' ' ' ''' blocks of size ''' ' ' 'num2str(blocksize) '  ''')'''  '])']);  
   elseif strcmp(opt,'b'),
      plot(index,theta)
   	title('Threshold decreasing from left to right');
		eval(['xlabel(''K''),' ' ylabel([texlabel(''theta'') ' '''   (''' ' num2str(k) ' ' ' ''' blocks of size ''' ' ' 'num2str(blocksize) '  ''')'''  '])']);  
   
   else
      error('3rd input should be one of ''t'' or ''b'' ')
   end

end
warning on