I have a time series and I would like to plot the pdf of an empirical and the lognormal distribution with the same mean and std deviation.
The code I am using is the following:
%SPX SPX=dataSet(:,2); [n,x] = hist(SPX,50); plot(x,n/10000/diff(x(1:2))) hold on m=mean(SPX) s=std(SPX) plot(x,normpdf(x,m,s),'r') hold on mu = m; sd = s; ix = -5*sd:1e-3:5*sd; iy = pdf('lognormal', ix, mu, sd); plot(ix,iy);
plotting the pdf of the empirical distribution seems to work, but I do not understand what the smaller figures, which looks more than a mountain than as a pdf, is showing me In addition, plotting a lognormal distribution with the same mean and std deviaton does no work. Does anybody have an idea what I am missing?
I suggest you plot the histogram this way:
n = n/length(SPX)/diff(x(1:2)); bar(x,n,'hist')
Then you plotted the normal distribution just fine. But for the lognormal distribution, the parameters are the mean and std of the log of the data. Try this:
mu = mean(log(SPX)); sd = std(log(SPX)); ix = linspace(min(SPX),max(SPX)); iy = pdf('lognormal', ix, mu, sd); plot(ix,iy,'g-');