What is it that I get from MATLAB function probplot?

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!

[Filip Trönnberg]

I call the function like this:

Alt 1: probplot('exponential', data)

Alt 2: probplot('weibull', data)

Answer 1

[Tom Lane]

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.

[Filip Trönnberg]

Really great explanation!! Now I get what I'm looking at! Thanks! :)

Just one question though; I know that the data most likely will not fit any distribution, but, would it be proper to say that the weibull distribution is a better fit than the exponential distribution in my case? Or am I grasping at straws here?

[bym]

Exponential distribution is a special case of Weibull, as is the Rayleigh distribution.

Better? maybe, depending on your definition. Good? - no

try lognormal

Answer 2

[Daniel Shub]

Basically, if your data came from the chosen distribution (exponential/Weibull) then the blue data points would overlap the dashed line. Since the dashed line does not predict the data in either the top or bottom plots, it means your data did not come from an exponential or Weibull distribution.