  The present paper gives a statistical adventure towards exploring the average
case complexity behavior of computer algorithms. Rather than following the
traditional count based analytical (pen and paper) approach, we instead talk in
terms of the weight based analysis that permits mixing of distinct operations
into a conceptual bound called the statistical bound and its empirical
estimate, the so called "empirical O". Based on careful analysis of the results
obtained, we have introduced two new conjectures in the domain of algorithmic
analysis. The analytical way of average case analysis falls flat when it comes
to a data model for which the expectation does not exist (e.g. Cauchy
distribution for continuous input data and certain discrete distribution inputs
as those studied in the paper). The empirical side of our approach, with a
thrust in computer experiments and applied statistics in its paradigm, lends a
helping hand by complimenting and supplementing its theoretical counterpart.
Computer science is or at least has aspects of an experimental science as well,
and hence hopefully, our statistical findings will be equally recognized among
theoretical scientists as well.
