Tailed
disTribuTions
Tailed distributions occupy a special position in pattern recognition. ey are used
to describe extreme events. e representation of such less likely events is not often
the primary interest of project managers and engineers. Attention to central ten-
dencies and overall generic expressions of dispersion have dominated managerial
thinking. e prediction of tails is a specialist domain, not a generalist’s credo. In
recent years, interest in tails has increased. Software buyers would like to estimate
residual defects. Business managers would like to estimate scope creep. Engineering
managers would like to predict size growth. Hence, models of software evolution
were created.
e following ve chapters are devoted to the use of a few tailed distributions:
log-normal, gamma, Weibull, Gumbel, and Gompertz. Each distribution has
unique characteristics that entail unique applications. Together, these ve distribu-
tions can handle most extreme events in software engineering. A remarkable appli-
cation of such distributions is in the construction of software reliability growth
models, described in Chapters 19 and 21.
Despite the mathematical form, which might dissuade a casual reader, these
distributions are simple to use; they are widely used in the industry. Computations
needed for solving these expressions are minimal and can be accomplished using
MS Excel.
iV
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