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The complex Watson distribution and shape analysis

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  • K. V. Mardia
  • I. L. Dryden

Abstract

The complex Watson distribution is an important simple distribution on the complex sphere which is used in statistical shape analysis. We describe the density, obtain the integrating constant and provide large sample approximations. Maximum likelihood estimation and hypothesis testing procedures for one and two samples are described. The particular connection with shape analysis is discussed and we consider an application examining shape differences between normal and schizophrenic brains. We make some observations about Bayesian shape inference and finally we describe a more general rotationally symmetric family of distributions.

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  • K. V. Mardia & I. L. Dryden, 1999. "The complex Watson distribution and shape analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 913-926.
    • Handle: RePEc:bla:jorssb:v:61:y:1999:i:4:p:913-926
    DOI: 10.1111/1467-9868.00210
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    Cited by:

    1. Frank G. Ball & Ian L. Dryden & Mousa Golalizadeh, 2008. "Brownian Motion and Ornstein–Uhlenbeck Processes in Planar Shape Space," Methodology and Computing in Applied Probability, Springer, vol. 10(1), pages 1-22, March.
    2. W. V. Félix de Lima & A. D. C. Nascimento & G. J. A. Amaral, 2021. "Entropy-based pivotal statistics for multi-sample problems in planar shape," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 153-178, March.
    3. Athanasios Micheas & Dipak Dey, 2005. "Assessing shape differences in populations of shapes using the complex watson shape distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(2), pages 105-116.
    4. Micheas, Athanasios C. & Dey, Dipak K., 2005. "Modeling shape distributions and inferences for assessing differences in shapes," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 257-280, February.
    5. Valdevino Félix de Lima, Wenia & David Costa do Nascimento, Abraão & José Amorim do Amaral, Getúlio, 2021. "Distance-based tests for planar shape," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    6. K. V. Mardia, 1999. "Directional statistics and shape analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(8), pages 949-957.
    7. Alshabani, A.K.S. & Dryden, I.L. & Litton, C.D., 2007. "Partial size-and-shape distributions," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1988-2001, November.

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