Abstract
This paper gives a broad overview of models for major discrete distributions such as binomial, negative binomial, Borel-Tanner and lost-games. Because the need lies not only in prediction problems but, perhaps even more so, in developing understanding and insight of natural phenomena, there has been increasing interest in identifying and developing models which give rise to various distributions. For example, see Bates and Neyman (1952), Haight (1961, 1965), Kemp and Kemp (1968, 1969, 1971), Boswell and Patil (1970, 1971, 1972), Patil and Boswell (1972), and Janardan (1973).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bates, Grace E. and Neyman, J. (1952). University of California Publications in Statistics, 1, 215–54.
Boswell, M.T. and Patil, G.P. (1970). In Random Counts in Scientific Work, Vol. 1, Random Counts in Models and Structures, G.P. Patil (ed.). The Pennsylvania State University Press, University Park, Pa. 3–22.
BoswelL, M.T. and Patil, G.P. (1971). In Statistical Ecology, Vol. 1, Spatial Patterns and Statistical Distributions, G.P. Patil et al. (eds.). The Pennsylvania State University Press, University Park, Pa. 97–127.
Boswell, M.T. and Patil, G.P. (1972). In Stochastic Point Processes, P.A.W. Lewis (ed.). Wiley, New York. 285–98.
Boswell, M.T. and Patil, G.P. (1973). Australian Journal of Statistics, 15, 128–31.
Cohen, J.E. (1971). Casual Groups of Monkeys and Men. Harvard University Press, Cambridge, Mass.
Consul, P.C. and Mittal, S.P. (1973). A new urn model with pre-determined strategy. Department of Mathematics, University of Calgary, Research Paper No. 214.
Feller, W. (1968). An Introduction to Probability Theory and its Applications, 3rd edition. Wiley, New York.
Haight, F.A. (1961). Biometrika, 48, 167–73.
Haight, F.A. (1965). Zastosowania Matematyki Applicationes Mathematicae, 8, 37–46.
Haight, F.A. and Breuer, M. (1960). Biometrika, 47, 143–50.
Hamdan, M.A. (1973). South African Statistical Journal, 7, 69–71.
Irwin, J.O. (1963). Journal of the Royal Statistical Society, series A, 126, 1–41.
Janardan, K.G. (1973a). Sankhya, Series A, 35.
Janardan, K.G. (1973b). Institute of Mathematical Studies Bulletin, 2, No. 6. (Abstract).
Janardan, K. G. and Patil, G. P. (1972). Sankhya, Series A, 34, 1–14.
Johnson, N.L. and Kotz, S. ( 1969, 1970, 1972). Distributions in Statistics (four volumes). Wiley, New York.
Kagan, Y.Y. (1973). Statistical methods in the study of seismic processes. Proceedings of the International Statistical Institute: Vienna, 1–15.
Kemp, A. W. and Kemp, C. D. (1968). Journal of the Royal Statistical Society, Series B, 30, 160–63.
Kemp, A.W. and Kemp, C.D. (1969). Journal of Applied Probability, 6, 700–03.
Kemp, A.W. and Kemp, C.D. (1971). Zastosowania Matematyki Applicationes Mathematicae, 12, 167–73.
Kemp, C.D. (1973). Accident Analysis and Prevention, 5, 371–73.
Kemp, C.D. (1967). Journal of the Statistical and Social Inquiry Society of Ireland, 21, 151–57.
Krishnamoorthy, A.S. (1951). Sankhya, 11, 117–24.
McKendrick, A.G. (1926). Proceedings of the Edinburgh Mathematical Society, 44, 98–130.
Mosimann, J.E. (1962). Biometrika, 49, 65–82.
Mosimann, J.E. (1963). Biometrika, 50, 47–54.
Ord, J.K. (1972). Families of Frequency Distributions. Griffin, London; Hafner, New York.
Patil,G.P. and Boswell,M.T. (1972). Sankhya, series A, 34, 293–96.
Patil, G.P. and Joshi, S.W. (1968). Dictionary and Bibliography of Discrete Distributions. Oliver & Boyd, Edinburgh; Hafner, New York.
Sibuya, M., Yosimura, I., and Shimizu, R. (1964). Annals of the Institute of Statistical Mathematics, 26, 409–15.
Teicher, H. (1954). Skandanavisk Aktuarietidskrift, 37, 1–9.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1975 D. Reidel Publishing Company, Dordrecht-Holland
About this paper
Cite this paper
Patil, G.P., Boswell, M.T. (1975). Chance Mechanisms for Discrete Distributions in Scientific Modeling. In: Patil, G.P., Kotz, S., Ord, J.K. (eds) A Modern Course on Statistical Distributions in Scientific Work. NATO Advanced Study Institutes Series, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1845-6_2
Download citation
DOI: https://doi.org/10.1007/978-94-010-1845-6_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-1847-0
Online ISBN: 978-94-010-1845-6
eBook Packages: Springer Book Archive