X = load('./data/islands.csv');
Y = log(X);
n= length(Y);

breaks = 2:10; 
counts = histc(Y, breaks);
hist(Y, 2.5:9.5);                 % this produces a desired histogram

cumul = cumsum(counts);

normQ = norminv( cumul/(n+1),0,1);    % standard normal quantiles

figure(2)
plot(breaks, normQ, '*');    % QQ plot based on "breaks"

normplot(Y)           % biult-in Matlab function. Has the same shape, but the Y-axis is labeled differently

qqplot(Y)                % another option, with axes switched

% -----------------------------------
%% QQplot of Ca + Mg, based on quantiles 
%

 X = load('./data/camg1.csv');
 ca020 = X(:,5);
 mg020 = X(:,6);
 
 scatter(ca020, mg020)
 
 decile1 = prctile(ca020, 0.1:0.1:0.9);
 decile2 = prctile(mg020, 0.1:0.1:0.9);
 
 plot(decile1, decile2,'*')
 
 %    Kolmogorov-Smirnov test
 % 
 
 muhat = mean(Y);
 sdhat = std(Y);
 Ysort = sort(Y);
 CDFfit = [Ysort normcdf(Ysort,muhat, sdhat)];
 
 [h, pvalue ,D, crit] = kstest(Y,CDFfit)   
             % KS test compares the emprical CDF of data Y to the suggested
             % CDFfit.
             % see Matlab help for a detailed explanation
   
  cdfplot(Y)
    hold on
   xc = 2:0.2:10;  
  plot(xc,  normcdf(xc,muhat, sdhat), 'red');
   hold off