MATLAB: What is it that I get from MATLAB function probplot

curve fittingfitfittingplottingprobability

I have a question regarding MATLAB's function 'probplot'. Say I have data and try to see if the data fit to some specific distribution and I get, say either Alt 1:
or Alt 2:
What can I then say about the results? I have read 'doc probplot' and I know that it says it gives a 'reference line useful for judging whether the data follow the given distribution'. I still find it hard to say anything moderately 'intelligent' about my two examples. Would really appreciate it if someone could give a good explanation of how the MATLAB function 'probplot' works!

Best Answer

Take a look at this for illustration of the mechanics of how the function works:
x = exprnd(2,20,1);
subplot(1,2,1); probplot('normal',x)
subplot(1,2,2); probplot('normal',x)
set(gca,'YTickLabelMode','auto')
set(gca,'YTickmode','auto')
ylabel('standard quantiles')
The plot on the left is the probability plot. The plot on the right is the same plot, but with all the special "probplot" stuff removed.
So by looking at the plot on the right, you can see it's your sorted data plotted against quantiles from a standard normal distribution. However, on the left you can see that the y axis scale has been changed to correspond to probability values from the normal distribution. Data from a non-standard normal distribution (other than mean 0, standard deviation 1) would have the same shape but the intercept and slope of the line would be different.
For some distributions like the Weibull one you showed, the x axis has a log scale. This is so different parameters would change only the intercept and slope.
Daniel gave a good answer related to the interpretation of the plot.
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