James E. Mosimann

Abstract Size-related shape changes in animals are studied within a general framework of size variables and shape vectors. Isometry, or independence of shape and size, is defined as the independence of some (all) shape vector(s) from a particular size variable. With mild restrictions it is shown that isometry is possible with respect to at most one size variable, or in other words that shape will always be related to a variety of size variables. The choice of a size variable is a hitherto neglected, but important, part of an allometric study. The use of functional relationships in allometry is contrasted with the approach developed here. Also, size and shape variables are used in characterizations of the lognormal, gamma and generalized gamma distributions. The results, given in a biological context, are of interest in size and shape studies generally.

An investigation of current American society's depiction of the ideal female body was performed. Body measurements of Playboy magazine centerfolds and Miss America contestants for 1979–1988 indicated body weight 13–19% below expected weight for women in that age group. Miss America contestants showed a significant decrease in expected weight between 1979 and 1988. Comparisons were made with an earlier study which had demonstrated that body measurements of both groups had decreased during the period 1959–1978. Diet-for-weight-loss and exercise articles in six women's magazines were tabulated for 1959–1988. A significant increase in both diet articles and exercise articles occurred during this period. These findings suggest that the overvaluation of thinness continues and thinness is now sought through both dieting and exercise.

Journal Article Canonical and principal components of shape Get access JOHN N. DARROCH, JOHN N. DARROCH School of Mathematical Sciences, Flinders UniversityAdelaide, S.A., 5042, Australia Search for other works by this author on: Oxford Academic Google Scholar JAMES E. MOSIMANN JAMES E. MOSIMANN Division of Computer Research and Technology, National Institute of HealthBethesda, Maryland 20014, U.S.A. Search for other works by this author on: Oxford Academic Google Scholar Biometrika, Volume 72, Issue 2, August 1985, Pages 241–252, https://doi.org/10.1093/biomet/72.2.241 Published: 01 August 1985 Article history Received: 01 July 1983 Revision received: 01 December 1984 Published: 01 August 1985

Abstract Concepts of independence for nonnegative continuous random variables, X 1, …, Xk , subject to the constraint ΣXi = 1 are developed. These concepts provide a means of modeling random vectors of proportions which is useful in analyzing certain kinds of data; and which may be of interest in quantifying prior opinions about multinomial parameters. A generalization of the Dirichlet distribution is given, and its relation to the Dirichlet is simply indicated by means of the concepts. The concepts are used to obtain conclusions of biological interest for data on bone composition in rats and scute growth in turtles.

On the compound multinomial distribution, the multivariate β-distribution, and correlations among proportions Get access JAMES E. MOSIMANN JAMES E. MOSIMANN National Institutes of HealthBethesda, Md. Search for other works by this author on: Oxford Academic Google Scholar Biometrika, Volume 49, Issue 1-2, 1962, Pages 65–82, https://doi.org/10.1093/biomet/49.1-2.65 Published: 01 June 1962