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Regression-based Approaches 163
11.5 REGRESSION-BASED APPROACHES
11.5.1 Probability plotting
There are many types of graphical procedures available for assessing goodness of fit.
The simplest of these involve plotting the EDF together with the hypothesized CDF
against the corresponding ordered sample data, x (i) . An example is shown in Figure
11.2(a). Such a plot can be used to visually examine distributional characteristics (such
as skewness and kurtosis) and to detect outliers and the presence of contamination
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(mixtures of distributions). However, the difficulty of assessing the GOF given the
curved nature of distribution functions has been widely acknowledged.
Probability plotting is an elegant graphical procedure which offers the advantage
of judging the goodness-of-fit based on a straight line. This is made possible by trans-
forming the EDF axis using special probability plotting paper such that the sample
observations should fall roughly in straight line if the hypothesized distribution ade-
quately represents the data. Different hypothesized models demand different types of
probability plotting papers. If the points on such a plot fall along a straight line on the
probability plotting paper, the underlying probability distribution can be considered
adequate for modeling the data. An example of probability plotting is shown in
Figure 11.2(b) alongside the simple procedure described in the previous paragraph.
It is relatively easier to judge the quality of a linear fit compared to a higher-order
nonlinear fit.
Probability plotting has been widely acknowledged as an extremely versatile and
useful tool as it not only provides a pictorial representation of data, but also allows
nonparametric estimation of the percentiles and other model parameters of the un-
derlying distributions. Furthermore, it can readily be used for censored observations
as commonly encountered in life-data analysis for reliability and survival analysis
applications.
In recent years, many statistical software programs have been developed to au-
tomate the probability plotting process. These include MINITAB, Statgraphics, and
JMP. In the absence of such automated means and probability plotting papers, normal
graph papers can be used, given the existence of simple linearizing transformations.
Such transformations are discussed here and demonstrated through the use of the

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Figure 11.2 (a) Simple graphical goodness-of-fit comparison. (b) Graphical goodness-of-fit
comparison using probability plotting on normal probability paper.