Weighted Mean Inactivity Time Function with Applications

Antonio Di Crescenzo () and Abdolsaeed Toomaj ()
Additional contact information
Antonio Di Crescenzo: Dipartimento di Matematica, Università degli Studi di Salerno, Via Giovanni Paolo II n. 132, I-84084 Fisciano, SA, Italy
Abdolsaeed Toomaj: Department of Mathematics and Statistics, Faculty of Basic Sciences and Engineering, Gonbad Kavous University, Gonbad 4971799151, Iran

Mathematics, 2022, vol. 10, issue 16, 1-30

Abstract: We consider an extension of the mean inactivity time based on a non-negative weight function. We show various properties of the new notion, and relate it to various functions of interest in reliability theory and information measures, such as the dynamic cumulative entropy, the past entropy, the varentropy, and the weighted cumulative entropy. Moreover, based on the comparison of weighted mean inactivity times, we introduce and study a new stochastic order and compare it with other suitable orders. We also discuss some results about the variance of transformed random variables and the weighted generalized cumulative entropy. Then, we investigate certain connections with the location-independent riskier order. Finally, we pinpoint several characterizations and preservation properties of the new stochastic order under shock models, random maxima, and notions of renewal theory.

Keywords: generalized cumulative entropy; lower record values; mean inactivity time; weighted mean inactivity time function; left spread function; renewal theory; variance (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/16/2828/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/16/2828/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:16:p:2828-:d:883755

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().