Abstract
Geologists unfamiliar with the application of probability theory to discrete data in other fields of research are usually acquainted with only three discrete theoretical frequency distributions: Poisson, binomial, and negative binomial distributions. In some situations these distributions may fail to adequately describe a set of experimental data. Other distributions such as the Poisson with zeros, Neyman type A, logarithmic with zeros, Poisson-binomial, and Thomas double Poisson together with the more common Poisson, binomial, and negative binomial form a generalized subset of discrete theoretical distributions, one of which should fit almost any experimental data set. A computer program is presented which allows testing of any combination of these distributions against observed discrete data.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bliss, C. I., and Fisher, R. A., 1953, Fitting the negative binomial distribution to biological data: Biometrics, v. 9, no. 2, p. 176–200.
Chakravarti, I. M., Laha, R. G., and Roy, J., 1967, Handbook of methods of applied statistics, v. 1: John Wiley & Sons, New York, 460 p.
Cohen, A. C., Jr., 1960, An extension of a truncated Poisson distribution: Biometrics, v. 16, no. 3, p. 446–450.
Douglas, J. B., 1955, Fitting the Neyman type A (two parameter) contagious distribution: Biometrics, v. 11, no. 1, p. 149–158.
Griffiths, J. C., 1967, Scientific methods in analysis of sediments: McGraw-Hill Book Company, New York, 508 p.
Harbaugh, J. W., and Bonham-Carter, G., 1970, Computer simulation in geology: John Wiley & Sons, New York, 575 p.
Katti, S. K., 1966, Interrelations among generalized distributions and their components: Biometrics, v. 22, no. 1, p. 44–52.
Lomnitz, C., 1966, Statistical prediction of earthquakes: Geophysics Rev., v. 4, p. 377–393.
McGuire, J. U., Brindley, T. A., and Bancroft, T. A., 1957, The distribution of corn borer larvaePyrausta nubilalis (HBN.), in field corn: Biometrics, v. 13, no. 1, p. 65–78.
Nielsen, K. L., 1964, Methods in numerical analysis: The MacMillan Company, New York, 408 p.
Ondrick, C. W., and Griffiths, J. C., 1969, Discrete distribution models of binomial, Poisson, and negative binomial: Kansas Geol. Survey Computer Contr. 35, 20 p.
Peizer, D. B., and Pratt, J. W., 1968, A normal approximation for binomial, F, beta and other common, related tail probabilities, I: Jour. Am. Stat. Assoc., v. 63, p. 1416–1456.
Pincus, H. J., 1953, The analysis of aggregates of orientation data in the earth sciences: Jour. Geology, v. 61, no. 6, p. 482–509.
Pratt, J. W., 1968, A normal approximation for binomial, F, beta, and other common, related tail probabilities, II: Jour. Am. Stat. Assoc., v. 63, p. 1457–1483.
Shaw, A. B., 1964, Time in stratigraphy: McGraw-Hill Book Co., New York, 365 p.
Shenton, L. R., 1949, On the efficiency of the method of moments and Neyman's type A distribution: Biometrika, v. 36, p. 450–454.
Steel, R. G., and Torrie, J. H., 1960, Principles and procedures of statistics: McGraw-Hill Book Company, New York, p. 395–397.
Thomas, Marjorie, 1949, A generalization of Poisson's binomial limit for use in ecology: Biometrika, v. 36, p. 18–25.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gates, C.E., Ethridge, F.G. A generalized set of discrete frequency distributions with Fortran program. Mathematical Geology 4, 1–24 (1972). https://doi.org/10.1007/BF02083189
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02083189