Abstract
This paper deals with a new system of discrete distributions. It also gives several characterizations of the Waring (and hence the Yule) distribution (and its truncated versions), the super-Poisson, the discrete uniform and other discrete distributions by using this system and other such systems existing in the literature, and linear regression. Continuous analogues of the above results are also briefly discussed.
Similar content being viewed by others
References
Bissinger, B. H. (1965). A type-resisting distribution generated from considerations of an inventory decision model, Classical and Contagious Discrete Distributions, (ed. G. P.Patil), 15–17, Statistical Publishing Society, Calcutta.
Irwin, J. O. (1965). Inverse factorial series as frequency distributions, Classical and Contagious Discrete Distributions (ed. G. P.Patil), 159–174, Statistical Publishing Society, Calcutta.
Johnson, N. L. and Kotz, S. (1969). Discrete Distributions, Houghton-Mifflin, Boston.
Johnson, N. L. and Kotz, S. (1970). Continuous Univariate Distributions—1, Wiley, New York.
Katz, L. (1945). Characteristics of frequency functions obtained by first order difference equations, Dissertation, University of Michigan.
Katz, L. (1965). Unified treatment of a broad class of discrete probability distributions, Classical and Contagious Discrete Distributions, (ed. G. P.Patil), 175–182, Statistical Publishing Society, Calcutta.
Krishnaji, N. (1970). A characteristic property of the Yule distribution, Sankhyā Ser. A, 32, 343–346.
Ord, J. K. (1967a). Graphical methods for a class of discrete distributions. J. Roy. Statist. Soc. Ser. A, 130, 232–238.
Ord, J. K. (1967b). On a system of discrete distributions, Biometrika, 54, 649–656.
Patil, G. P. and Joshi, S. W. (1968). A Dictionary and Bibliography of Discrete Distributions, Oliver & Boyd, Edinburgh.
Patil, G. P. and Rao, C. R. (1977). The weighted distributions: A survey of their applications, Applications of Statistics, (ed. P. R.Krishnaiah), 383–405, North-Holland, Amsterdam.
Rao, C. R. (1965). On discrete distributions arising out of methods of ascertainment, Classical and Contagious Discrete Distributions, (ed. G. P.Patil), 320–332, Statistical Publishing Society, Calcutta.
Xekalaki, E. (1983). A property of the Yule distribution and its applications, Comm. Statist. A—Theory Methods, 12, 1181–1188.
Author information
Authors and Affiliations
About this article
Cite this article
Korwar, R.M. On a new system of discrete distributions and characterizations of several discrete distributions by equality of distributions. Ann Inst Stat Math 41, 305–321 (1989). https://doi.org/10.1007/BF00049398
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00049398