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Quantal models: a review with additional methodological development

Fieller, N. and Cankaya, E. (2009) Quantal models: a review with additional methodological development. Journal of Applied Statistics, 36 (4). pp. 369-384. ISSN 0266-4763

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Analysis of quantal models is a particular aspect of the general problem of investigating multimodality. The distinction is that the spacings between modes are integral multiples of some unspecified fundamental unit and that the number of modes is not defined. Such semi-structured models arise in a wide variety of contexts such as biology, cosmology, archaeology and molecular physics. This paper presents a brief review of their historical development in such areas as an aid to their recognition in other contexts as well as giving guidance to their analysis from the statistical viewpoint. The available methodology for their analysis is collated into a coherent and self-contained account, establishing various optimality properties under particular parametric distributional assumptions. An illustrative power study shows how dependence on sample size and failure of assumptions such as underlying distribution, origin of measurements and independence affect the power of various analyses. These aspects are illustrated by an example from developmental biology.

Item Type: Article
Keywords: cosine quantogram; megalithic yard; quantal model; multimodality; power
Institution: The University of Sheffield
Academic Units: The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)
Depositing User: Mrs Megan Hobbs
Date Deposited: 22 Mar 2010 16:10
Last Modified: 16 Nov 2015 11:48
Published Version: http://dx.doi.org/10.1080/02664760802466195
Status: Published
Publisher: Taylor & Francis
Identification Number: 10.1080/02664760802466195
URI: http://eprints.whiterose.ac.uk/id/eprint/10609

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