Summary
The intent of this paper is to provide an anthology of results on the subject of models (chance mechanisms) that give rise to the Univariate Generalized Waring Distribution. These include results that have appeared in the statistical literature before as well as some new ones that appear for the first time in this paper. Some characterization problems relating to certain genesis schemes are also considered.
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
Bardwell, G. E. and Crow, E. L. (1964). A two parameter family of hyper-Poisson distributions. Journal of the American Statistical Association, 59, 133–141.
Bhattacharya, S. K. (1966). Confluent hypergeometric distributions of discrete and continuous type with applications to accident proneness. Bulletin of the Calcutta Statistical Association, 15, 20–21.
Bissinger, B. H. (1965). A type resisting distribution generated from considerations of an inventory decision model. In Classical and Contagious Discrete Distributions, G. P. Patil, ed. Pergamon Press and Statistical Publishing Society, Calcutta, Pages 15–17.
Dacey, M. F. (1969). A hypergeometric family of discrete probability distributions: Properties and applications to location models. Geographical Analysis, 1, 283–317.
Davies, O. L. (1933). On asymptotic formulae for the hyper-geometric series. Biometrika, 25, 295–322.
Davies, O. L. (1934). On asymptotic formulae for the hyper-geometric series. Biometrika, 26, 59–107.
Erdélyi, A. et al. (1953). Higher Transcendental Functions, Vol. 1. McGraw-Hill, New York.
Feller, W. (1968). An Introduction to Probability Theory and its Applications, Vol. 1. Wiley, New York.
Friedman, B. (1949). A simple urn model. Communications on Pure and Applied Mathematics, 2, 59–70.
Haight, F. A. (1966). Some statistical problems in connection with word association data. Journal of Mathematical Psychology, 3, 217–233.
Herdan, G. (1964). Quantitative Linguistics. Butterworths, London.
Irwin, J. O. (1963). The place of mathematics in medical and biological statistics. Journal of the Royal Statistical Society, Series A, 126, 1–44.
Irwin, J. O. (1968). The generalized Waring distribution applied to accident theory. Journal of the Royal Statistical Society, Series A, 131, 205–225.
Irwin, J. O. (1975). the generalized Waring distribution. Journal of the Royal Statistical Society, Series A,138, 18–31 (Part I), 204–227 (Part II), 374–384 (Part III).
Janardan, K. G. (1973). Chance mechanisms for multivariate hypergeometric models. Sankhya, Series A, 35, 465–478.
Janardan, K. G. and Patil, G. P. (1972). A unified approach for a class of multivariate hypergeometric models. Sankhya, Series A, 34, 363–376.
Johnson, N. L. and Kotz, S. (1977). Urn Models and Their Application. Wiley, New York.
Jordan, C. (1927). Sur un cas généralisé de la probabilité des épreuves répétées. Acta Scientiarum Mathematicarum, 3, 193–210.
Kemp, A. W. (1968a). A wide class of discrete distributions and the associated differential equations. Sankhyá, Series A, 30, 401–410.
Kemp, A. W. (1968b). A limited risk cPp. Skandinavisk Aktuarietidskrift, 51, 198–203.
Kemp, A. W. and Kemp, C. D. (1968). On a distribution associated with certain stochastic processes. Journal of the Royal Statistical Society, Series B, 30, 160–163.
Kemp, A. W. and Kemp, C. D. (1971). On mixing processes and the lost-games distribution. Zastosowania Matematyki, 12, 167–173
Kemp, A. W. and Kemp, C. D. (1975). Models for Gaussian hypergeometric distributions. In Statistical Distributions in Scientific Work, Vol. 1, G. P. Patil, S. Kotz and J. K. Ord, eds. Reidel, Dordrecht-Holland. Pages 31–40.
Kemp C. D. and Kemp, A. W. (1956). Generalized hypergeometric distributions. Journal of the Royal Statistical Society, Series B, 18, 202–211.
Kendall, M. G. (1961). Natural law in the social sciences. Journal of the Royal Statistical Society, Series A, 124, 1–16.
Krishnaji, N. (1970). A characteristic property of the Yule distribution. Sankhya, Series A, 32, 343–346.
Sarkadi, K. (1957). Generalized hypergeometric distributions. A Magyar Tudományos Akadémia Matematikai Kutaté Intézet Közleményei, 2, 59–69.
Shimizu, R. (1968). Generalized hypergeometric distributions. Proceedings of the Institute of Statistical Mathematics, 16, 147–165 (in Japanese).
Shimura, T. and Takahasi, K. (1967). On the moments and the examples of the distribution of the time to extinction in the Galton-Watson process. Proceedings of the Institute of Statistical Mathematics, 15, 161–166 (in Japanese)
Sibuya, M. and Shimizu, R. (198Oa). Classification of the Generalized Hypergeometric Family of Distributions. (Monograph in preparation).
Sibuya, M. and Shimizu, R. (198Ob). What are the generalized hypergeometric distributions? (To appear).
Simon, H. A. (1955). On a class of skew distribution functions. Biometrika, 42, 425–440.
Simon, H. A. (1960). Some further notes on a class of skew distribution functions. Information and Control, 3, 80–88.
Skibinsky, M. (1970). A characterization of hypergeometric distributions. Journal of the American Statistical Association, 65, 926–929.
Xekalaki, E. (1980). On an inventory model with a Yule demand distribution. Research Report No. EXO1,Statistics and Operations Research Laboratory, Trinity College, Dublin.
Yule, G. W. (1924). A mathematical theory of evolution based on the conclusions of Dr. J. C. Willis, F.R.S. Philosophical Transactions of the Royal Society of London, Series B, 213, 21–87.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1981 D. Reidel Publishing Company
About this paper
Cite this paper
Xekalaki, E. (1981). Chance Mechanisms for the Univariate Generalized Waring Distribution and Related Characterizations. In: Taillie, C., Patil, G.P., Baldessari, B.A. (eds) Statistical Distributions in Scientific Work. NATO Advanced Study Institutes Series, vol 79. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-8549-0_12
Download citation
DOI: https://doi.org/10.1007/978-94-009-8549-0_12
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-8551-3
Online ISBN: 978-94-009-8549-0
eBook Packages: Springer Book Archive