A Note on NBUE and NWBUE Classes of Life Distributions
M. Z. Anis

TL;DR
This paper explores non-monotonic ageing classes of life distributions, specifically NBUE and NWBUE, providing new results, counterexamples, and corrections to existing notions in reliability theory.
Contribution
It extends the understanding of NBUE and NWBUE classes by presenting new properties, counterexamples, and corrections for these non-monotonic ageing notions.
Findings
Some properties of NBUE carry over to NWBUE
Counterexamples show moment bounds do not transfer
Corrective results for NWBUE notions are provided
Abstract
Non-monotonic ageing notions are looked upon as an extension of the corresponding monotonic ageing notions in this work. In particular, the New Better than Used in Expectation (NBUE) and the corresponding non-monotonic analogue New Worse then Better than Used in Expectation (NWBUE) classes of life distributions is considered. Some additional results for the NBUE class are obtained. While many properties of the NBUE class carry over in an analogous way to the NWBUE class, it is shown by means of counterexamples that the moment bounds do not. Some corrective results with respect to popular notions of the NWBUE class are also presented.
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Taxonomy
TopicsStatistical Distribution Estimation and Applications · Insurance, Mortality, Demography, Risk Management · Probability and Risk Models
