Computational Statistics

112 COMPARISONS

For the comparison of two samples the corresponding function qqplot() can be used: if we de-

note the empirical quantiles by Y

1,(i:n)

resp. Y

2,(i:n)

, the plot is the graph

`

Y

1,(i:n)

, Y

2,(i:n)

´

i=1...n

in the case of equal sample sizes. The necessary caution we mentioned above comes in if the

sample sizes differ. If the sample sizes differ, R generates nodes by linear interpolation, with

the smaller of the two sample sizes determining the number of nodes.

The P P plot does not have equivariance properties comparable to those of the QQ. If we want to

eliminate scale and shift parameters, we have to transform the data first. Mathematical theory ...