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On weak convergence within a Lorenz ordering family of distributions

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

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

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