Advertisement

Statistics and Computing

, Volume 14, Issue 1, pp 53–57 | Cite as

Simulation for the complex Bingham distribution

  • John T. Kent
  • Patrick D.L. Constable
  • Fikret Er
Article

Abstract

The complex Bingham distribution is relevant for the shape analysis of landmark data in two dimensions. In this paper it is shown that the problem of simulating from this distribution reduces to simulation from a truncated multivariate exponential distribution. Several simulation methods are described and their efficiencies are compared.

acceptance-rejection complex Bingham distribution landmark data shape analysis simulation truncation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Dagpunar J. 1988. Principles of Random Variate Generation. Clarendon Press, Oxford.Google Scholar
  2. Devroye L. 1986. Non-Uniform Random Variate Generation. Springer-Verlag, New York.Google Scholar
  3. Dryden I.L. and Mardia K.V. 1998. Statistical Shape Analysis. Wiley, Chichester.Google Scholar
  4. Kent J.T. 1994. The complex Bingham distribution and shape analysis. J. R. Statist. Soc. B 56:285-299.Google Scholar
  5. Kinderman A.J. and Monahan J.F. 1977. Computer generation of random variables using the ratio of uniform deviates. ACM Transactions on Mathematical Software, 3: 257-260.Google Scholar
  6. Kinderman A.J. and Monahan J.F. 1980. New methods for generating Student's tand gamma variables. Computing 25: 369-377.Google Scholar
  7. Leydold J. 2000. Automatic sampling with the ratio-of-uniforms method. ACM Transactions on Mathematical Software 26: 78-98.Google Scholar
  8. Stuart A. and Ord J.K. 1994. Kendall's Advanced Theory of Statistics, Volume I: Distribution Theory, 6th ed. Arnold, London.Google Scholar
  9. von Neumann J. 1963. Various techniques used in connection with random digits. In: A.H. Taub (Ed.), CollectedWorks, vol. 5. Pergamon Press, Oxford, pp. 768-770.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • John T. Kent
    • 1
  • Patrick D.L. Constable
    • 2
  • Fikret Er
    • 3
  1. 1.Department of Statistics, School of MathematicsUniversity of LeedsLeedsUK
  2. 2.Sherborne, DorsetUK
  3. 3.Department of Statistics, Faculty of ScienceAnadolu UniversityEskişehirTurkey

Personalised recommendations