A model for the statistical distribution of microlithotypes in coal

  • Murray A. Cameron
  • John W. Hunt


Microlithotype composition of a coal sample is often summarized by examining a large number (~500) of subsamples of a grain mount and estimating proportions of vitrite, intermediates, and inertite, where, for samples we have investigated, the proportion of intermediates is generally less than 0.4. This suggests that most subsamples are either greater than 95% vitrinite or greater than 95% inertinite, so that the statistical distribution of vitrinite has most of its weight in its tails. Two distributions which may have this shape are the beta and the logistic normal, and these have been fitted to the microlithotype distribution of some coal samples. Parameters of these fitted distributions are related to the proportion of vitrinite in the sample and thickness of microscopic bands in the coal. For coals in the Sydney Basin, at least, it was found that the parameter relating to band thickness is approximately constant over a coal seam; therefore, fitting one or other of these distributions to such data leads to directly interpretable parameters.

Key words

β distribution coal microlithotypes compositional data logistic normal distribution petrography 


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  1. Aitchison, J., 1982, The statistical analysis of compositional data: Jour. Roy. Stat. Soc. Ser. B., v. B44, p. 139–177.Google Scholar
  2. Bennett, A. J. R., 1974, Coal petrology and its application to seam evaluation,in, Geology and Geophysics in Coal Exploration and Mining: Australian Mineral Foundation Inc, Adelaide, p. 139–168.Google Scholar
  3. Hacquerbard, P. A., Birmingham, T. F., and Donaldson, J. R., 1967, Petrography of Canadian coals in relation to environment of deposition,in, Symposium on Science and Technology of Coal, Ottawa, p. 84–97.Google Scholar
  4. International Committee for Coal Petrology (ICCP), 1963, International handbook of coal petrology, 2nd ed., Centre National de la Recherche Scientifique, Paris.Google Scholar
  5. Johnson, N. L., 1949, Systems of frequency curves generated by methods of translation: Biometrika, v. 36, p. 149–176.Google Scholar
  6. Johnson, N. L. and Kotz, S., 1970, Distributions in statistics: Continuous univariate distributions 2: John Wiley & Sons, New York, 306 p.Google Scholar
  7. Nelder, J. A. and Mead, R., 1965, A simplex method for function minimization: Comput. Jour., v. 7, p. 308–313.Google Scholar
  8. Smyth, M., 1974, The relationship between coal macerals and microlithotypes: CSIRO Mineral Research Laboratories, investigation report 105, 22 p.Google Scholar
  9. Standards Association of Australia, 1977, Preparation of hard coal samples for microscopical examination by reflected light: Australian Standard 2061, 10 p.Google Scholar
  10. Tukey, J. W., 1977, Exploratory data analysis: Addison Wesley, Reading, Pennsylvania, 688 p.Google Scholar

Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • Murray A. Cameron
    • 1
  • John W. Hunt
    • 2
  1. 1.CSIRO Division of Mathematics and StatisticsLindfieldAustralia
  2. 2.CSIRO Division of Fossil FuelsNorth RydeAustralia

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