Statistics of Shape, Direction and Cylindrical Variables

Authors: K. V. Mardia¹; J. Kirkbride¹; F. L. Bookstein²

Source: Journal of Applied Statistics, Volume 31, Number 4, May 2004 , pp. 465-479(15)

Publisher: Routledge, part of the Taylor & Francis Group

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Abstract:

In statistical shape analysis, the shape of an object is understood to be what remains after the effects of location, scale and rotation are removed. We consider the distributional problem of triangular shape and an associated direction; motivated by a data set of microscopic fossils. We begin by constructing a parallel transport system such that the data transform onto the space S²×S². A joint shape distribution on S²×S¹ is proposed based on Jupp & Mardia's bivariate distribution on S²×S¹. For concentrated data, an approximation to the distribution on S²×S¹ is given by a distribution on R¹×S¹, and we explore a distribution on this space by extending Mardia & Sutton's distribution on R²×S¹. In this distribution, the expected edgel direction varies linearly in the shape coordinates. This is found to be a useful model for the microfossil data.

Keywords: Bookstein coordinates; edgel; Fisher distribution; Kendall coordinates; microfossil data; triangle shape; von Mises distribution

Document Type: Research article

DOI: http://dx.doi.org/10.1080/02664760410001681756

Affiliations: 1: University of Leeds, Leeds, UK 2: University of Michigan, Ann Arbor, USA

Publication date: 2004-05-01

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