The description, interpretation, and curve fitting of the negative binomial distribution has become a topic of great interest to American acturaries in the last few years. What is it? Where did it come from? What does it mean? How can it be used? These and many other questions have been asked by all of us. The first thing to do, of course, is to check the textbooks and references in our personal
... [Show full abstract] libraries. After this has been done, some questions may still remain or some new ones brought to mind. The purpose of this paper is to present a bibliography selected especially for actuaries from the hundreds of papers and texts that deal with the subject, to organize the material, and to make a few comments on each reference so that the interested reader may choose those references which are of particular interest to him and study them in detail. Two mechanical models are also described which may be used by the reader to actually generate negative binomial distributions. II. THE FUNDAMENTALS If only one paper can be read, it should be Arbous and Kerrich.' The first part is a critical evaluation and gives a good description in non-mathematical terms of the accident proneness concept. The significant literature on the subject up to 1951 is reviewed. These authors force us to separate the con-cepts of accident proneness and accident liability. Accident proneness is an attribute of the individual which does not fluctuate and does not tend to increase or decrease over a long period of time. Accident liability includes accident proneness plus the effects of age, experience, fatigue, emotional state, general health, and so forth. In the mathematical section of the paper the negative binomial is developed and discussed from two viewpoints. If See Appendix A "Selected Bibliography" for complete citation of this and other refer-ences throughout the paper.