Summary
This paper is concerned with properties of the univariate generalized Waring distribution such as infinite divisibility, discrete self-decomposability, completeness and regression.
Similar content being viewed by others
References
Bondesson, L. (1979). On the infinite divisibility of products of powers of gamma variables,Zeit. Wahrscheinlichkeitsth.,37, 171–175.
Bondesson, L. (1979). On generalized gamma and generalized negative binomial convolutions. Part I.Scand. Actuarial J., 125–146.
Forst, G. (1979). A characterization of self-decomposable probabilities on the half-line,Zeit. Wahrscheinlichkeitsth.,49, 349–352.
Haight, F. A. (1966). Some statistical problems in connection with word association data,J. Math. Psychol.,3, 217–233.
Irwin, J. O. (1963). The place of mathematics in medical and biological statistics,J. R. Statist. Soc., A,126, 1–44.
Irwin, J. O. (1968). The generalized Waring distribution applied to accident theory,J. R. Statist. Soc., A,131, 205–225.
Irwin, J. O. (1975). The generalized Waring distribution,J. R. Statist. Soc., A,138, 18–31 (Part I), 204–227 (Part II), 374–384 (Part III).
Kendall, M. G. (1961). Natural law in the social sciences.J. R. Statist. Soc., A,124, 1–16.
Korwar, R. M. (1975). On characterizing some discrete distributions by linear regression,Commun. Statist.,4, 1133–1147.
Korwar, R. M. (1977). On characterizing Lagrangian Poisson and quasi-binomial distributions,Commun. Statist., A,6, 1409–1415.
Shimizu, R. (1968) Generalized hypergeometric distributions,Proc. Inst. Statist. Math.,16, 147–164 (in Japanese).
Sibuya, M. (1979). Generalized hypergeometric, digamma and trigamma distributions,Ann. Inst. Statist. Math.,31, A, 373–390.
Sibuya, M. and Shimizu, R. (1981). Classification of the generalized hypergeometric family of distributions,Keio Science and Technology Reports,34, 1–38.
Simon, H. A. (1955). On a class of skew distribution functions,Biometrika,42 425–440.
Steutel, F. W. and van Harn, K. (1979). Discrete analogues of self-decomposability and stability,Ann. Prob.,7, 893–899.
Thorin, O. (1977). On the infinite divisibility of the Pareto distribution,Scand. Actuarial J., 31–40.
Xekalaki, E. (1977). Bivariate and multivariate extensions of the generalized Waring distribution, Ph.D. thesis University of Bradford, UK.
Xekalaki, E. (1977). On characterizing the bivariate Poisson, binomial and negative binomial distributions,Analytic Function Methods in Probability Theory (Colloq. Math. Soc. J. Bolyai, 21) (ed. B. Gyires), North Holland, 1980, 369–379.
Xekalaki, E. (1979). A characterization of the negative hypergeometric distribution based on conditional expectation,Proceedings of the Sixth Conference on Probability Theory, Brasov, Romania (eds. B. Bereanu et al.), Editure Academii Republicii Socialiste Romania, 1981, 379–384.
Xekalaki, E. (1980). The univariate generalized Waring distribution in relation to accident theory. Proneness, spells or contagion?Technical Report No. 100, Dept. of Statistics, University of Missouri, Columbia, USA,Biometrics (to appear).
Xekalaki, E. (1981). Chance mechanisms for the univariate, generalized Waring distribution and related characterizations,Statistical Distributions in Scientific Work, (Models, Structures and Characterizations) (eds. C. Taillie, G. P. Patil and B. Baldessari), D. Reidel, Holland,4, 157–171.
Author information
Authors and Affiliations
About this article
Cite this article
Xekalaki, E. Infinite divisibility, completeness and regression properties of the univariate generalized waring distribution. Ann Inst Stat Math 35, 279–289 (1983). https://doi.org/10.1007/BF02480983
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02480983