Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

The figure shows the Q-Q plot of a theoretical and empirical standardized Normal distribution generated through the $qqnorm()$ function of R statistical tool.

enter image description here

How can I describe the right tail (top right) that does not follow the red reference line? What does it mean when there is a "trend" that running away from the line?

Thank you

share|improve this question
1  
While I think the question is OK for math.SE, it would even be better on stats.SE . –  Raskolnikov Aug 26 '11 at 11:24
    
Ok thank you, i also had the doubt..! Ok if i'm not lucky here i will post it on stats.SE :) –  Maurizio Aug 26 '11 at 12:01
    
Could this be a software bug? –  Michael Hardy Aug 26 '11 at 16:25
    
What R commands did you use to get the "theoretical quantiles"? –  Michael Hardy Aug 26 '11 at 16:26
    
I see: that's built in to the qqnorm command. But when I tried this, I got respectable-looking results. –  Michael Hardy Aug 26 '11 at 16:32
show 2 more comments

2 Answers

up vote 4 down vote accepted

It means that in the right tail, your data do not fit normal well, specifically, there are far less numbers there would be in a normal sample. If the black curved up, there would be more than in a typical normal sample.

You can think of the black curve as a graph of a function that , if applied to your data, would make them like a normal sample.

In the following image, random sample is generated by applying Ilmari Karonen's function to normal sample.

Screen shot of Mathematica session

share|improve this answer
    
thank you! Please correct me if i say something wrong. In my case in the right tail of my distribution (sample quantiles) i have less numbers than the theoretical one (theoretical quantiles) because the "black points" curve down. I don t want to make confusione with the axis :) –  Maurizio Aug 26 '11 at 12:51
    
And suppose that i can count the values of my distribution, in the right tail of data sample distribution i will have a small number of values than the values in the theoretical normal distribution. That is what the qq-plot says..Sorry for the explanation of the first elementary school. –  Maurizio Aug 26 '11 at 12:55
1  
@Maurizio You got it right, I am merely rephrasing your statement to make it slightly more precise. The count of points at the right extreme in your data is lower, than expected in a sample drawn from normal distribution. –  Sasha Aug 26 '11 at 14:31
add comment

Looks like your data has a cutoff at $4$. You could probably fit the samples you plotted fairly well with a curve such as

$$y = \frac 1 2 \left( x + 4 - \sqrt{c+(x-4)^2} \right),$$

where $c > 0$ is a free parameter that describes the sharpness of the cutoff. Just by eyeballing the graph, I'd guess that $c \approx 0.1$ for your data.

share|improve this answer
    
Thank you! but if i only want to explain in words what should I say? for example, that, respect to the theoretical one, there is a bigger probability to have data in the right tail of my empirical normal distribution? (But anyway there is not a problem in goodness of fit tests, i ve already verified!) –  Maurizio Aug 26 '11 at 11:58
    
@Maurizio: I'm no statistician, but I'd just say that the real data is not quite normally distributed because it has a (soft) cutoff at 4. Since the cutoff is quite far out in the tail of the distribution, I suppose it doesn't affect the fit much. Do you have any idea what might be causing it? –  Ilmari Karonen Aug 26 '11 at 12:07
    
i don t know why, i'm analyzing the distribution of a voip traffic generator that should follows a normal distribution but first i have to understand how can i "read" the qq plots :) –  Maurizio Aug 26 '11 at 13:20
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.