Characterization Results on Lifetime Distributions by Scaled Reliability Measures Using Completeness Property in Functional Analysis

Mohamed Kayid and Mansour Shrahili ()
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Mohamed Kayid: Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Mansour Shrahili: Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Mathematics, 2023, vol. 11, issue 6, 1-15

Abstract: In this article, using the scaled (weighted) residual life variable, some scaled measures, the scaled mean residual life and the scaled hazard rate, are introduced. Several scales are considered as examples of the derivation of the scaled measures. The measures are developed for the case of a weighted residual life at a random time, and it is shown that the measures are scale-free in these cases. This property proves useful in situations where a relative comparison of the lifetime distribution is studied. Some characterization properties are derived in terms of scaled measures evaluated at some sequences of random time points that follow a typical distribution. Examples are used to illustrate, examine, and satisfy the obtained characterizations.

Keywords: hazard rate; mean residual lifetime; characterization; residual lifetime (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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