Exploratory Data Analysis
1.3. EDA Techniques
1.3.3. Graphical Techniques: Alphabetic
188.8.131.52. Normal Probability Plot
|Normal Probability Plot for Data with Long Tails||
The following is a normal probability plot of 500 numbers generated
from a double exponential distribution. The
double exponential distribution is symmetric, but relative to the
normal it declines rapidly and has longer tails.
We can make the following conclusions from the above plot.
For data with long tails relative to the normal distribution, the
non-linearity of the normal probability plot can show up in two ways.
First, the middle of the data may show an S-like pattern. This is
common for both short and long tails. In this particular case,
the S pattern in the middle is fairly mild. Second, the first few and
the last few points show marked departure from the reference fitted
line. In the plot above, this is most noticeable for the first few
data points. In comparing this plot to the
short-tail example in the previous section,
the important difference is the direction of the departure from the
fitted line for the first few and the last few points. For long
tails, the first few points show increasing departure from the
fitted line below the line and last few points show increasing
departure from the fitted line above the line. For short
tails, this pattern is reversed.
In this case we can reasonably conclude that the normal distribution can be improved upon as a model for these data. For probability plots that indicate long-tailed distributions, the next step might be to generate a Tukey Lambda PPCC plot. The Tukey Lambda PPCC plot can often be helpful in identifying an appropriate distributional family.