JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARYThe Hermite distribution is the generalized Poisson distribution whose probability generating function (P.G.F.) is exp [a1(s -1) + a2(s2 -1)]. The probabilities (and factorial moments) can be conveniently expressed in terms of modified Hermite polynomials (hence the proposed name). Writing these in confluent hypergeometric form leads to two quite different representations of any particular probability-one a finite series, the other an infinite series.The cumulants and moments are given. Necessary conditions on the parameters and their maximum-likelihood estimation are discussed.It is shown, with examples, that the Hermite distribution is a special case of the Poisson Binomial distribution (n = 2) and may be regarded as either the distribution of the sum of two correlated Poisson variables or the distribution of the sum of an ordinary Poisson variable and an (independent) Poisson 'doublet' variable (i.e. the occurrence of pairs of events is distributed as a Poisson).Lastly its use as a penultimate limiting form of distributions with P.G.F. exp a (si-1)is examined.

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xii + 344 pp. L24.95/$39.95. ISBN 0-521-57095-6.The titles of many books contain one or other of the phrases "mat hematical mode( 1) ling" or "statistical model( 1) ing" in their title. The doubled ell commonly indicates a European author; on both sides of the Atlantic, however, statisticians tend to equate "mathematical" with deterministic and "statistical" with stochastic. This well-written volume will widen the horizons of all those statisticians who think that "model-(1)ing" is merely about building a model, either deterministic or stochastic.Gershenfeld begins with an introductory chapter that discusses, inter alia, various levels of description for model building: specific versus general; model estimation versus firstprinciples models; numerical versus analytical; stochastic versus deterministic; microscopic versus macroscopic; discrete versus continuous; and qualitative versus quantitative. He is quick to point out that in each case there is a continuum of choices rather than a discrete choice. "These", he says, "are meta-modeling questions. There are no rigorous ways to make these choices, but once they've been decided there are rigorous ways to use them."A blunter title would have been 'The Methodology of Modeling'. The present title and the attractive cover and typography do much to ensure that the book falls into hands that need it, but might not realize that they need it. Once opened in the anticipation of a collection of well-presented and enter-taining case studies, the reader will soon realize that this is a book to keep and treasure for its very wide (but far from shallow), systematic overview of modelling techniques.There are three parts, four appendices, a bibliography, and an index. Part 1 looks at Analytical Models. "These are models that you can at least in theory write down with nothing more than a pencil and a piece of paper, hopefully arriving at an explicit closed-form solution." The four chapters are: 2,