thesis - Faculty of Information and Communication Technologies ...

Chapter 5. Growth Dynamics
bution parameters as they summarise the data and can gain an insight
into the evolution by observing changes to the distribution parameters
over time.
Some of the early work on understanding object-oriented software metric
data by fitting it to a distribution was conducted by Tamai et al.
[269,270] who have observed that the size of methods and classes (measured
using lines of code) within a hierarchy fit the negative-binomial
distribution. Recently, researchers inspired by work in complex systems
[209, 287] (especially, real-world networks) have attempted to understand
software metric distributions as power-laws. Baxter et al. [21]
studied 17 metrics in a number of Java software systems and have
shown that some metrics fit a log-normal distribution, while others fit
a power-law distribution, and also that some metrics did not fit either
of these distributions. Potanin et al. [223] investigated object graphs by
analysing run-time data, and found that incoming and outgoing references
fit a power law distribution. Wheeldon et al. [299] investigated the
Java Development Kit and found 12 metrics fit power-law distribution.
In a detailed case study of Visual Works Smalltalk, Java Development
kit and Eclipse IDE, Concas et al. [54] observe that out-degree measures
of the class graphs and Class Lines of Code fit a log-normal distribution,
while method lines of code and in-degree measures of a class graph fit a
Pareto distribution. Herraiz [118] investigated the distribution of SLOC
(Source Lines of Code) in 12,010 packages available for the FreeBSD
software system and found that SLOC fitted a double pareto distribution.
The common element in all of these studies is that software metric
distributions are non-gaussian and tended to be positively skewed with
long tails. Unfortunately, these studies have not been able to identify
a consistent probability distribution that can be expected for a certain
metric.
Despite consistent results that find skewed distributions when a robust
fit is found, the methods used to fit the distributions have certain
inherent weaknesses and limitations. In order to fit many of these distributions,
the raw data is often transformed since software metric data
has a large number of zero values. For instance, it is common to have a
set of classes with no dependents or methods with no branching state-
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