thesis - Faculty of Information and Communication Technologies ...

Chapter 5. Growth Dynamics
• How does the profile and shape of this distribution change as software
systems evolve?
• Is the rate and nature of change erratic?
• Do large and complex classes become bigger and more complex as
software systems evolve?
The typical method to answer these questions is to compute traditional
descriptive statistical measures such as arithmetic mean (referred to as
“mean” in the this thesis to improve readability), median and standard
deviation on a set of size and complexity measures and then analyze
their changes over time. However, it has been shown that software size
and complexity metric distributions are non-gaussian and are highly
skewed with long tails [21, 55, 270]. This asymmetric nature limits
the effectiveness of traditional descriptive statistical measures such as
mean and standard deviation as these values will be heavily influenced
by the samples in the tail making it hard to derive meaningful inferences.
Recently advocated alternative method to analyze metric distributions
[21,55,118,223,270,299] involves fitting metric data to a known probability
distribution. For instance, statistical techniques can be used to
determine if the metric data fits a log-normal distribution [55]. Once a
strong fit is found, we can gain some insight into the software system
from the distribution parameters. Unfortunately, the approach of fitting
data to a known distribution is more complex and the metric data
may not fit any known and well understood probability distributions
without a transformation of the data.
Software metrics, it turns out, are distributed like wealth in society —
where a few individuals have a high concentration of wealth, while the
majority are dispersed across a broad range from very poor to what
are considered middle class. To take advantage of this nature, we analyze
software metrics using the Gini coefficient, a bounded higher-order
statistic [191] widely used in the field of socio-economics to study the
distribution of wealth and how it changes over time. Specifically it is
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