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Measures of ageing tendency

Part of: Survival analysis and censored data Distribution theory Distribution theory - Probability

Published online by Cambridge University Press:  30 July 2019

Magdalena Szymkowiak
Magdalena Szymkowiak*
Affiliation:
Poznan University of Technology
*
*Postal address: Institute of Automation and Robotics, Poznan University of Technology, Pl. M. Skłodowskiej-Curie 5, 60-965 Poznań, Poland.
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Abstract

A family of generalized ageing intensity functions of univariate absolutely continuous lifetime random variables is introduced and studied. They allow the analysis and measurement of the ageing tendency from various points of view. Some of these generalized ageing intensities characterize families of distributions dependent on a single parameter, while others determine distributions uniquely. In particular, it is shown that the elasticity functions of various transformations of distributions that appear in lifetime analysis and reliability theory uniquely characterize the parent distribution. Moreover, the recognition of the shape of a properly chosen generalized ageing intensity estimate admits a simple identification of the data lifetime distribution.

Keywords

Generalized failure rategeneralized ageing intensityelasticity functioncharacterization

MSC classification

Primary: 60E05: Distributions
Secondary: 62E10: Characterization and structure theory 62N05: Reliability and life testing
Type
Research Papers
Information
Journal of Applied Probability , Volume 56 , Issue 2 , June 2019 , pp. 358 - 383
Copyright
© Applied Probability Trust 2019 

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