%Illustrates the chi-squared PDF for different degrees of freedom.
%Not the PDF is normalized in each case to have a mean value of one.

clear; 

figure(2); clf; hold on; 

col='krybmcgkrybmcgkry';
df=.001; 
for ct=2:2:20;
  vals=df/2:df:5*ct; 
  pdf=chi2pdf(vals,ct);
  cdf=chi2cdf(vals,ct);
  pl=find(cdf<=0.025); 
  ci(1)=vals(pl(end))/ct;
  fill([vals(pl)/ct fliplr(vals(pl)/ct) vals(1)],[zeros(1,length(pl)) fliplr(ct*pdf(pl)) ct*pdf(1)],col(ct/2));    
  pl=find(cdf>=0.975);
  ci(2)=vals(pl(1))/ct;
  fill([vals(pl)/ct fliplr(vals(pl)/ct) vals(pl(1))/ct],[zeros(1,length(pl)) fliplr(ct*pdf(pl)) ct*pdf(pl(1))],col(ct/2)); 
  h=plot(vals/ct,ct*pdf,col(ct/2));
  set(h,'linewidth',2); 

  h=ylabel('probability'); font(h,16); 
  h=xlabel('power density'); font(h,16); 
  font(gca,16); 
  if ct==2;
    axis([0 5 0 1.5]); 
  else;
    axis([0 5 0 1.5]);
  end;
  title(['modified \chi^2 probability density function with ',num2str(ct),' degrees of freedom']);
  [ci; chi2confPH(0.95,ct)],
  pause; 
end;