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Chapter 5. Growth Dynamics
ments. These zero values need to be eliminated as log-normal, pareto
and power-law distributions only work with data that has positive values.
However, the impact of these transformations, if any, is not properly
represented in the studies [21, 54, 223, 270, 299]. Furthermore,
once data is transformed, this aspect has to be considered when deriving
any inferences. Recently, a weakness of the approach with respect
to fitting power-laws has been put forward by Goldstein et al. [104] as
well as Clauset et al. [48]. They argue that the widely used approach
of fitting power laws using a graphical linear fit of data transformed
into a log-log scale is biased and inaccurate, especially since there is
no quantitative measure of the goodness-of-fit that is used in this approach.
This limitation would apply to the work by Wheeldon et al. [299]
as they use a direct linear-fit of the log-log plot of the full raw histogram
of the data. Potanin et al. [223] and Concas et al. [55] also use a linear
fit of the logarithmically binned histogram which limits the power and
conclusions in their studies [48].
Another limitation is that we cannot use these distributions for a meaningful
comparison between software systems or different releases of the
same software system. This is because the distributions are created
by estimating the parameters from the underlying raw data rather than
from empirically derived tables. Further, the value of fitting metric data
to known distributions in order to infer the underlying generative process
has not yet been properly established [210], especially since multiple
non-correlated processes have been shown to generate the same
distribution. Interestingly, this limitation is acknowledged by Concas
et al. [54, 55], but they present their work of fitting metric data to a
distribution as valuable since it provides a broad indication of a potential
underlying process and more importantly can indicate presence
of extreme values. A similar argument is also extended by Valverde et
al. [287]. The common approach used by these studies based on the
analysis of a metric data distribution is to infer the underlying generative
process by investigating a single release. For instance, Concas et
al. [55] argue that the presence of these skewed distributions in software
denotes that the programming activity cannot be considered to be
a process involving random addition of independent increments but exhibits
strong organic dependencies on what has been already developed.
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