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Simulation of a Bayesian Interval Estimate for a Heterogeneity Measure

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Compstat

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Abstract

A well-known measure of the heterogeneity of a population is provided by the statistic

$$H = - \sum\limits_{i = 1}^s {{p_i}\log {p_i}}$$

where it is assumed that s possible categories have respective probabilities Pi…, Ps.

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References

  1. Boender, C.G.E. and Rinnooy, Kan, A.H.G. (1987) A multinomial Bayesian approach to the estimation of population and vocabulary size, Biometrika, 74, pp. 849–856.

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  2. Engen, S. (1978) Stochastic abundance models. Chapman and Hall, London.

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  3. Gill, C.A. and Joanes, D.N. (1979) Bayesian estimation of Shannon’s index of diversity, Biometrika, 66, 1, pp. 81–85.

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  4. Good, I.J. (1966) How to estimate probabilities, Journal of the Institute of Mathematics and its Applications, 2, pp. 364–383.

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  5. Joanes, D.N. and Gill, C.A. (1992) Interval estimation of a measure of diversity, Journal of Applied Statistics, 19, 3, pp. 323–327.

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  6. Patil, G.P. and Taillie, C. (1982) Diversity as a concept and its measurement, Journal of the American Statistical Association, 77, pp.548567.

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  7. Pielou, E.C. (1975) Ecological Diversity. Wiley, New York.

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Author information

Authors and Affiliations

  1. Department of Statistics, University of Leeds, UK

    Derrick N. Joanes, Christine A. Gill & Andrew J. Baczkowski

Authors
  1. Derrick N. Joanes
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  2. Christine A. Gill
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  3. Andrew J. Baczkowski
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Editor information

Editors and Affiliations

  1. Department for Statistics and Probability Theory, University of Technology Vienna, Wiedner Hauptstraße 8-10, A-1040, Vienna, Austria

    Rudolf Dutter

  2. Department of Statistics, OR and Computer Science, University Vienna, Universitätsstraße 5, A-1010, Vienna, Austria

    Wilfried Grossmann

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© 1994 Springer-Verlag Berlin Heidelberg

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Joanes, D.N., Gill, C.A., Baczkowski, A.J. (1994). Simulation of a Bayesian Interval Estimate for a Heterogeneity Measure. In: Dutter, R., Grossmann, W. (eds) Compstat. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-52463-9_20

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  • DOI: https://doi.org/10.1007/978-3-642-52463-9_20

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-0793-6

  • Online ISBN: 978-3-642-52463-9

  • eBook Packages: Springer Book Archive

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