Titel_SS06

Now by plotting x against,-1(()FxX ), see also Figure 2.18 it is seen that a straight line is
obtained with slope depending on the standard deviation of the random variable X and
crossing point with the y-axis depending on the mean value of the random variable. Such a
plot is sometimes called a quantile plot, see also Section 2.6.

0.84

0.02

0.98

0.999

0.001

0.5

0.16

1.0

-1.0

2.0

3.0

-3.0

0.0

-2.0

x

FxX^ -1(())FxX

Figure 2.18: Illustration of the non-linear scaling of the y-axis for a Normal distributed random
variable.

Also in Figure 2.18 the scale of the non-linear y-axis is given corresponding to the linear
mapping of the observed cumulative probability densities. In probability papers typically only
this non-linear scale is given.

Probability papers may also be constructed graphically. In Figure 2.19 the graphical
construction of a Normal probability paper is illustrated.

-3 -2 -1 0 1 2 3

0.001

0.159 0.159

0.001

0.5 0.5

0.841 0.841

0.999

0.999

-3 -2 -1 0 1 2 3

x

x

FX(x)

FX(x)

Figure 2.19: Illustration of the graphical construction of a Normal distribution probability paper.

Various types of probability paper are readily available in the literature.