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 Craig system. 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.