Thesaurus of univariate discrete probability distributions
The Thesaurus presents the most comprehensive overview in the field of discrete probability distributions. It contains 750 univariate discrete distributions (fully indexed with all names by which they are known), presenting their probability (mass) function, the support, the parameter space and the probability generating function.
For each distribution its relations (identities, reparametrisations, special cases, convergences, family memberships) to the other ones are provided in the book and elaborated in detail. A full list of references is appended to each distribution. The bibliography at the end of the book contains more than 4000 items.
The book can be used both by theoreticians striving for generalizations (there is a separate list of families of distributions, and the families are presented in full extent) and by empirical scientists searching for generating mechanisms or models of their data.
Research results in the Thesaurus are in many cases complementary to the monograph „Univariate Discrete Distributions“ (Second Edition) by N.L. Johnson, S. Kotz and A.W. Kemp. Two hundred distributions contained in the Thesaurus have been used to form a separate publication accompanied by a software („Altmann-Fitter – Iterative fitting of probability distributions“).
As one of the basic mathematical handbooks the Thesaurus of univariate discrete probability distributions should be accessible in any scientific library.
Thesaurus of univariate discrete probability distributions by Gejza Wimmer & Gabriel Altmann, STAMM Verlag GmbH Essen, 1st ed. 1999, XXVII + 838 pages, paperback.ISBN: 3-87773-025-6.
Gejza Wimmer, mathematical statistician at the Institute of Mathematics of the Slovak Academy of Sciences, Bratislava, Slovakia, author of a text-book and numerous articles on distributions and their application in social and natural sciences.
Gabriel Altmann, retired mathematical linguist (University of Bochum, Germany) author of two volumes on distributions, numerous articles on their application in linguistics and a software helping to fit them to empirical data.