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On weak convergence within a Lorenz ordering family of distributions

Part of: Probability theory on algebraic and topological structures Distribution theory

Published online by Cambridge University Press:  14 July 2016

Gwo Dong Lin
Gwo Dong Lin*
Affiliation:
Academia Sinica, Taiwan
*
∗Postal address: Institute of Statistical Science, Academia Sinica, Taipei 11529, Taiwan, Republic of China.
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Abstract

We first introduce a Lorenz ordering family of distributions which are related to the gamma distribution, and then prove that the weak convergence within this family is equivalent to the convergence of each moment sequence of positive orders to the corresponding moment of the limiting distribution.

Keywords

WEAK CONVERGENCECHARACTERIZATION OF DISTRIBUTIONGAMMA DISTRIBUTION

MSC classification

Primary: 60B10: Convergence of probability measures
Secondary: 62E10: Characterization and structure theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 4 , December 1995 , pp. 1028 - 1031
Copyright
Copyright © Applied Probability Trust 1995 

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References

Arnold, B. C. (1987) Majorization and the Lorenz Order: A Brief Introduction. Lecture Notes in Statistics 43, Springer-Verlag, Berlin.Google Scholar
Arnold, B. C. (1991) Preservation and attenuation of inequality as measured by the Lorenz order. In Stochastic Orders and Decision under Risk, ed. Mosler, K. and Scarsini, M. IMS Lecture Notes Monograph Series. 19, USA.CrossRefGoogle Scholar
Basu, S. K. and Bhattacharjee, M. C. (1984) On weak convergence within the HNBUE family of life distributions. J Appl. Prob. 21, 654–660.CrossRefGoogle Scholar
Chow, Y. S. and Teicher, H. (1988) Probability Theory, 2nd edn. Springer-Verlag, New York.CrossRefGoogle Scholar
Shiryayev, A. N. (1984) Probability, Translated by Boas, R. P. Springer-Verlag, New York.Google Scholar
Shorack, G. R. and Wellner, J. A. (1986) Empirical Processes with Applications to Statistics. Wiley, New York.Google Scholar
Stoyan, D. (1983) Comparison Methods for Queues and Other Stochastic Models. Wiley, New York.Google Scholar