Hostname: page-component-7b7567c8c-2n9c9 Total loading time: 0 Render date: 2026-11-15T08:48:55.528Z Has data issue: false hasContentIssue false
  • English
  • Français

Random mappings with an attracting center: Lagrangian distributions and a regression function

Published online by Cambridge University Press:  14 July 2016

Sven Berg and
Ljuben Mutafchiev
Sven Berg*
Affiliation:
Lund University
Ljuben Mutafchiev*
Affiliation:
Bulgarian Academy of Sciences
*
∗ Postal address: Department of Statistics, University of Lund, Box 7008, S-220 07 Lund, Sweden.
∗∗ Postal address: Bulgarian Academy of Sciences, Institute of Mathematics, 1090 Sofia P.O. Box 373, Bulgaria.
Get accessRights & Permissions [Opens in a new window]

Abstract

For a random mapping model with a single attracting center (Stepanov (1971)) we study the relationship between the sizes of the central tree, the adjacent points, and the free points. Joint, marginal and conditional distributions are shown to be of well-known Lagrangian type. Exact and asymptotic moment properties are investigated with the aid of Riordan's (1968) Abel identities. In particular, the relationship between the size of the central tree and that of the central component is discussed in terms of a regression function.

Keywords

RANDOM GRAPHSLIMITING DISTRIBUTIONSREGRESSION

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 3 , September 1990, pp. 622 - 636
Copyright
Copyright © Applied Probability Trust 1990 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

Partial financial support for this research was obtained from the Swedish Council for the Humanities and Social Sciences, and from the Committee of Sciences, Bulgarian Council of Ministers, Contract No. 60.

References

Berg, S. and Jaworski, J. (1988) Modified binomial and Poisson distributions with applications in random mapping theory. J. Statist. Planning Inf. 36, 313–322.Google Scholar
Consul, P. C. (1974) A simple urn model dependent upon predetermined strategy. Sankhya B 36, 391–399.Google Scholar
Consul, P. C. (1975) Some new characterizations of discrete Lagrangian distributions. In Statistical Distributions in Scientific Work, Vol. 3, ed. Patii, G. P. et al., D. Reidel, Dordrecht, 279–290.Google Scholar
Consul, P. C. and Jain, G. C. (1973) A generalization of the Poisson distribution. Technometrics 15, 791–799.Google Scholar
Feller, W. (1951) An Introduction to Probability Theory and its Applications, Vol. 1, 2nd edn. Wiley, New York.Google Scholar
Gupta, A. C. (1977) Minimum variance unbiased estimation in a modified power series distribution. Commun. Statist. – Theory Methods 6, 977–991.Google Scholar
Harris, B. (1960) Probability distributions related to random mappings. Ann. Math. Statist. 31, 1045–1061.CrossRefGoogle Scholar
Jaworski, J. (1984) On a random mapping (T, Pj). J. Appl. Prob. 21, 186–191.Google Scholar
Kolchin, V. F. (1986) Random Mappings. Optimization Software, New York.Google Scholar
Mutafchiev, L. (1987) On random mappings with a single attracting centre. J. Appl. Prob. 24, 258–264.CrossRefGoogle Scholar
Riordan, J. (1968) Combinatorial Identities. Wiley, New York.Google Scholar
Stepanov, V. E. (1971) Random mappings with a single attracting centre. Theory Prob. Appl. 16, 155–161.Google Scholar