Abstract
The method of maximum likelihood used in analyzing data which are bimodal in the range (0, π)is lengthy and not always successful. Two alternative methods are proposed and the results compared with those obtained by using the method of maximum likelihood on orientation data from clasts and shells. It is shown that a procedure based on the Method of Moments gives comparable results and is much more practicable.
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References
Blatt, H., Middleton, G., and Murray, R., 1972, Origin of sedimentary rocks: Prentice-Hall, Englewood Cliffs, New Jersey, 634 p.
Clark, M. W., 1976, Some Methods for statistical analysis of multimodal distributions and their application to grain-size data: Jour. Intern. Assoc. Math. Geol., v. 8, p. 267–282.
Dempster, A., Laird, N. M., and Rubin, D. B., 1977, Maximum likelihood from incomplete data via the EM algorithm: Jour. Royal Stat. Soc., Ser. B, v. 39, p. 1–38 (with discussion).
Hartley, M. J., 1978, Comment on paper by Quandt and Ramsey: Jour. Amer. Stat. Ass., v. 73, p. 738–741.
Hasselblad, V., 1966, Estimation of parameters for a mixture of normal distributions: Technometrics, v. 8, p. 431–444.
Jones, T. A., and James, W. R., 1969, Analysis of bimodal orientation data: Jour. Intern. Assoc. Math. Geol., v. 1, p. 129–135.
Kelling, G. and Moshrif, M. A., 1977, The orientation of fossil bivalves in a pene-littoral sequence (the Rhaetian of South Wales): Jour. Sed. Pet., v. 47, no. 3, p. 1342–1346.
Kelling, G. and Williams, P. F., 1967, Flume studies of the reorientation of pebbles and shells: Jour. Geology, v. 75, no. 3, p. 243–267.
Mardia, K. V., 1972, Statistics of directional data: Academic Press, London and New York, 357 p.
Mardia, K. V. and Spurr, B. D., 1973, Multi-sample tests for multi-modal and axial circular populations: Jour. Royal Stat. Soc., Ser. B, v. 35, p. 422–436.
Pearson, K., 1894, Contributions to the mathematical theory of evolution: Phil. Trans. Royal Soc., Ser. A, v. 185, p. 71–110.
Quandt, R. E. and Ramsey, J. B., 1978, Estimating mixtures of normal distributions and switching regressions: Jour. Amer. Stat. Ass., v. 73, p. 730–752 (with discussion).
Stephens, M. A., 1969, Techniques for directional data: Tech. Report No. 150. Department of Statistics, Stanford University, California.
Unrug, R., 1957, Recent transport and sedimentation of gravels in the Dunajec valley (Western Carpathians): Acta Geologica Polonica, v. 7, p. 217–257.
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Spurr, B.D. On estimating the parameters in mixtures of circular normal distributions. Mathematical Geology 13, 163–173 (1981). https://doi.org/10.1007/BF01031392
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DOI: https://doi.org/10.1007/BF01031392