Summary
Any rock may be regarded as an “aggregate” of mineral species frequency distributions, thus opening up a new method of analyzing the problems of the nature of these discrete distributions.
Based on theorems in mathematical probability, a “subrock” sample is defined as a probability sample under the conditions that every mineral species' distribution function in this subrock converges probabilistically to one and the same distributions the nature of which is immaterial at this point.
For obvious reasons, the situation is excluded if the sample size approaches infinity, i.e., Chebyshev's theorem (Chebyshev, 1867).
This is a preview of subscription content, log in via an institution to check access.
References
Chebyshev, P. L., 1867, O srednih velisinah: Mat. Sbornik, no. 2: v. 2, p. 1–9.
Cramér, H., 1946, Mathematical methods of statistics: Princeton Univ. Press, 575 p.
Elderton, W. P., 1938, Frequency curves and correlation (3rd ed.): Cambridge Univ. Press, 271 p.
Elderton, W. P., and Johnson, N. L., 1969, Systems of frequency curves: Cambridge Univ. Press, 216 p.
Fréchet, M. M., 1929, Sur la convergence probable, read by E. Borel, C. R. l'Acad. Sci. Paris, hebdomadaires: v. 188, p. 213–214.
Fréchet, M. M., 1930, Sur la convergence “en probabilité”: Metron, v. 8, no. 4, p. 3.
Kolmogorov, A. N., 1933, Grundlagen der Wahrscheinlichkeits = Theorie (Am. ed.): Chelsea, New York, 70 p.
Lévy, P., 1935, Propriétés, asymptotiques des sommes de variables aléatoires indépendantes au enchainées: Jour. Math., Ser. 9, v. 14, p. 347–402.
Okamoto, M., 1959, A convergence theorem for probability distributions: Am. Inst. Stat. Math., v. 11, p. 107–112.
Pearson, K., 1894, Contribution to the mathematical theory of evolution: Phil. Trans. Roy. Soc. A., London, v. 185, p. 71–110.
Pearson, K., 1895, Contribution to the mathematical theory of evolution., 2: skew variation in homogeneous materials: Phil. Trans. Roy. Soc. A., London, v. 186, p. 343–414.
Scheffé, H., 1947, A useful convergence theorem for probability distributions: Ann. Math. Stat., v. 18, p. 434–438.
Slutsky, E., 1925, Über stochastische Asymptoten und Grenzwerte: Metron, v. 5, no. 3, p. 3–89.
Vistelius, A. B., 1967, Studies in mathematical geology: Consultants Bureau, New York, 294 p.
Zodrow, E. L., 1967, Statistical and geological reviews of the grading model of the Smallwood Mine, Labrador: unpubl. masters thesis, Pennsylvania State Univ.
Zodrow, E. L., 1968, The magnetite distribution in the Smallwood Mine: Can. Min. and Metall. Bull., v. 61, no. 673, p. 629–632.
Zodrow, E. L., 1970, Factor analyses and magnetite formation and distribution in the Smallwood Mine: AIME Trans., v. 247, p. 61–69.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zodrow, E.L., Sutterlin, P.G. Toward a definition of a mineral sample in geology. Mathematical Geology 3, 313–316 (1971). https://doi.org/10.1007/BF02045798
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02045798