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The hazard and vitality measures of ageing

Published online by Cambridge University Press:  14 July 2016

Joseph Kupka  and
Sonny Loo
Joseph Kupka
Affiliation:
Monash University
Sonny Loo*
Affiliation:
Monash University
*
∗Postal address for both authors: Department of Mathematics, Monash University, Clayton, VIC 3168, Australia.
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Abstract

A new measure of the ageing process called the vitality measure is introduced. It measures the ‘vitality' of a time period in terms of the increase in average lifespan which results from surviving that time period. Apart from intrinsic interest, the vitality measure clarifies the relationship between the familiar properties of increasing hazard and decreasing mean residual life. The main theorem asserts that increasing hazard is equivalent to the requirement that mean residual life decreases faster than vitality. It is also shown for general (i.e. not necessarily absolutely continuous) distributions that the properties of increasing hazard, increasing failure rate, and increasing probability of ‘sudden death' are all equivalent.

Keywords

MEAN RESIDUAL LIFEIHRDMRL
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 3 , September 1989 , pp. 532 - 542
Copyright
Copyright © Applied Probability Trust 1989 

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