Abstract
Statistical models underlying the analysis of orientation data commonly assume a unimodal symmetric population, such as the circular normal distribution. If the sample distribution is skewed or bimodal, standard procedures usually produce misleading results. Where such situations occur, a mixture of two or more circular normal distributions may be used as the population model. The parameters describing each mode and the mixing proportion may be estimated by the method of maximum likelihood using numerical techniques. This approach is applied to a distinctly bimodal set of cross-bedding data from the Mississippian Salem Limestone of central Indiana.
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References
Bowman, F., 1958, Introduction to Bessel functions: Dover Publications, Inc., New York, 135 p.
Curray, J. R., 1956, The analysis of two-dimensional orientation data: Jour. Geology, v. 64, no. 2, p. 117–131.
Greenwood, J. A., and Durand, D., 1955, The distribution of length and components of the sum of random unit vectors: Ann. Math. Stat., v. 26, p. 233–246.
Gumbel, E. J., Greenwood, J. A., and Durand, D., 1953, The circular normal distribution: Jour. Am. Stat. Assoc., v. 49, p. 267–297.
Hasselblad, V., 1966, Estimation of parameters for a mixture of normal distributions: Technometrics, v. 8, p. 431–444.
Jones, T. A., 1968, Statistical analysis of orientation data: Jour. Sed. Pet., v. 38, no. 1, p. 61–67.
Kelly, L. G., 1967, Handbook of numerical methods and applications: Addison-Wesley, Reading, Massachusetts, 354 p.
Krumbein, W. C., 1939, Preferred orientation of pebbles in sedimentary deposits: Jour. Geology, v. 47, no. 7, p. 673–706.
Lindgren, B. W., 1960, Statistical theory: The Macmillan Company, New York, 427 p.
Pincus, H. J., 1953, The analysis of aggregates of orientation data in the earth sciences: Jour. Geology, v. 61, no. 6, p. 482–509.
Pincus, H. J., 1956, Some vector and arithmetic operations on two-dimensional orientation variates, with applications to geologic data: Jour. Geology, v. 64, no. 6, p. 533–557.
Sedimentation Seminar, 1966, Cross-bedding in the Salem Limestone of central Indiana: Sedimentology, v. 6, no. 2, p. 95–114.
Steinmetz, R., 1962, Analysis of vectorial data: Jour. Sed. Pet., v. 32, no. 4, p. 801–812.
Tanner, W. F., 1955, Paleogeographic reconstructions from cross-bedding studies: Am. Assoc. Petroleum Geologists Bull., v. 39, no. 12, p. 2471–2483.
Tanner, W. F., 1959, The importance of modes in cross-bedding data: Jour. Sed. Pet., v. 29, no. 2, p. 221–226.
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Jones, T.A., James, W.R. Analysis of bimodal orientation data. Mathematical Geology 1, 129–135 (1969). https://doi.org/10.1007/BF02048557
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DOI: https://doi.org/10.1007/BF02048557