×

On weighted measure of inaccuracy for doubly truncated random variables. (English) Zbl 1421.94020

Summary: Recently, authors have studied the weighted version of Kerridge inaccuracy measure for left/right truncated distributions. In the present communication we introduce the notion of weighted interval inaccuracy measure and study it in the context of two-sided truncated random variables. In reliability theory and survival analysis, this measure may help to study the various characteristics of a system/component when it fails between two time points. We study various properties of this measure, including the effect of monotone transformations, and obtain its upper and lower bounds. It is shown that the proposed measure can uniquely determine the distribution function and characterizations of some important life distributions have been provided. This new measure is a generalization of recent weighted residual (past) inaccuracy measure.

MSC:

94A17 Measures of information, entropy
62N05 Reliability and life testing
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Arnold B.C., Pareto Distributions (1983) · Zbl 1169.62307
[2] DOI: 10.1109/TIT.1968.1054185 · doi:10.1109/TIT.1968.1054185
[3] DOI: 10.1016/0020-0255(91)90027-R · Zbl 0716.94003 · doi:10.1016/0020-0255(91)90027-R
[4] Cox D.R., J. R. Stat. Soc. 21 pp 411– (1959)
[5] Di Crescenzo A., Scientiae Mathematicae Japonicae 64 pp 255– (2006)
[6] DOI: 10.1080/03610929808832134 · Zbl 0900.62534 · doi:10.1080/03610929808832134
[7] Kerridge D.F., J. R. Stat. Soc. 23 pp 184– (1961)
[8] DOI: 10.1007/s00184-010-0315-7 · Zbl 1241.62014 · doi:10.1007/s00184-010-0315-7
[9] DOI: 10.1007/BF03263532 · Zbl 1301.62104 · doi:10.1007/BF03263532
[10] DOI: 10.1007/s10492-014-0080-4 · Zbl 1340.60013 · doi:10.1007/s10492-014-0080-4
[11] DOI: 10.1007/s00362-014-0600-z · Zbl 1319.60033 · doi:10.1007/s00362-014-0600-z
[12] Misagh F., In: Proc. ICMS 10, Ref. No. 100196, (2010)
[13] DOI: 10.1016/j.spl.2010.11.006 · Zbl 1205.62154 · doi:10.1016/j.spl.2010.11.006
[14] DOI: 10.3390/e14030480 · Zbl 1306.62214 · doi:10.3390/e14030480
[15] Nair K.R.M., IAPQR Trans. 25 (1) pp 1– (2000)
[16] DOI: 10.1007/BF02613380 · Zbl 0162.51101 · doi:10.1007/BF02613380
[17] DOI: 10.1109/24.556594 · Zbl 04536917 · doi:10.1109/24.556594
[18] DOI: 10.1080/03610928608829345 · Zbl 0609.62022 · doi:10.1080/03610928608829345
[19] DOI: 10.1002/j.1538-7305.1948.tb01338.x · Zbl 1154.94303 · doi:10.1002/j.1538-7305.1948.tb01338.x
[20] DOI: 10.1080/03610920802455001 · Zbl 1165.62009 · doi:10.1080/03610920802455001
[21] Taneja H.C., Kybernetika 22 pp 393– (1986)
[22] Weiner N., Cybernetics (1949)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.