# plot the distribution of a dataset

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Locks am 6 Mai 2013
Hi,
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?
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### Akzeptierte Antwort

Tom Lane am 7 Mai 2013
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-');
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Tom Lane am 8 Mai 2013
When I run your code I see a histogram with a green normal density superimposed. When I run histfit with the same number of bins, I see the same histogram with the same density, but red instead of green.
If you want a smooth density function that is like the histogram, try the ksdensity function. You could superimpose that over both the histogram and the normal density if you like.
Locks am 10 Mai 2013
ksdesity was excatly what I was looking for, thanks!!

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