There are a great many named
theoretical distributions but
a large proportion of them have
no known justification for their
existence. There are two main
reasons for this. First, it is
very easy to create a "new"
theoretical distribution or family
of distributions. For many years
any such "creation"
was sufficient to achieve an academic
publication. Second, no one ever,
to our knowledge, acted upon the
most elementary principles that
might afford some justification
for a proposed suggestion: namely,
does the new distribution provide
a good fit to some observed data
that cannot be fitted by the standard,
better known distributions? The
result is that periodicals are
full of suggested theoretical
distributions that in many cases
are of breathtaking worthlessness.
This set of two books attempts
to remedy this situation:
1. A very large number of theoretical
distributions is repeatedly fitted
to some 200 observed distributions.
2. I do not hesitate to conclude
that a distribution is without
value in fitting. Examples are
McKay's Bessel function distributions,
Fisher's quartic exponential distribution,
most of Johnson's system, a distribution
due to Ramberg et al.
3. I emphasize some theoretical
distributions of major usefulness
in fitting which do not seem to
be so well known among practitioners.
Examples are the immensely powerful
Kapteyn system, the Burr distribution,
the Evered distribution, and the
4. My goal throughout is to enable
any practitioner to be able to
recognize the most likely possibilities
as theoretical distributions for
his or her observed dist and to
eliminate the unlikely ones without
waste of time.