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On weak convergence within the hnbue family of life distributions

Published online by Cambridge University Press:  14 July 2016

Sujit K. Basu  and
Manish C. Bhattacharjee
Sujit K. Basu
Affiliation:
Indian Institute of Management, Calcutta
Manish C. Bhattacharjee*
Affiliation:
Indian Institute of Management, Calcutta
*
∗Postal address for both authors: Indian Institute of Management Calcutta, Joka, P. O. Box No. 16757, Alipore Post Office, Calcutta 700 027, India.
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Abstract

We show that the HNBUE family of life distributions is closed under weak convergence and that weak convergence within this family is equivalent to convergence of each moment sequence of positive order to the corresponding moment of the limiting distribution. A necessary and sufficient condition for weak convergence to the exponential distribution is given, based on a new characterization of exponentials within the HNBUE family of life distributions.

Keywords

EXPONENTIAL DISTRIBUTIONS
Type
Short Communications
Information
Journal of Applied Probability , Volume 21 , Issue 3 , September 1984 , pp. 654 - 660
Copyright
Copyright © Applied Probability Trust 1984 

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Footnotes

∗

Research supported by the Centre for Management and Development Studies at the Indian Institute of Management Calcutta under grant 491/CMDS-APRP-II.

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