×

zbMATH — the first resource for mathematics

A dynamic measure of inaccuracy between two past lifetime distributions. (English) Zbl 1216.62156
Summary: We introduce a dynamic measure of inaccuracy between two past life time distributions over the interval \((0,t)\). Based on the proportional reversed hazard rate model (PRHRM), a characterization problem for this dynamic inaccuracy measure has been studied. An upper bound to the dynamic measure of inaccuracy \(H^*(f,g;t)\) has also been derived.

MSC:
62N05 Reliability and life testing
62E10 Characterization and structure theory of statistical distributions
62B10 Statistical aspects of information-theoretic topics
PDF BibTeX Cite
Full Text: DOI
References:
[1] Di Crescenzo A, Longobardi M (2002) Entropy-based measure of uncertainty in past lifetime distributions. J Appl Probab 39: 434–440 · Zbl 1003.62087
[2] Di Crescenzo A, Longobardi M (2004) A measure of discrimination between past lifetime distributions. Stat Probab Lett 67: 173–182 · Zbl 1058.62088
[3] Ebrahimi N (1996) How to measure uncertainty about residual lifetime. Sankhya Ser A 58: 48–57 · Zbl 0893.62098
[4] Ebrahimi N, Kirmani SNUA (1996a) A measure of discrimination between two residual life-time distributions and its applications. Ann Inst Stat Math 48(2): 257–265 · Zbl 0861.62063
[5] Ebrahimi N, Kirmani SNUA (1996b) A characterization of the proportional hazards model through a measure of discrimination between two residual life distributions. Biomertika 83(1): 233–235 · Zbl 0865.62075
[6] Ebrahimi N, Pellerey F (1995) New partial ordering of survival functions based on notation of uncertainty. J Appl Probab 32: 202–211 · Zbl 0817.62082
[7] Gupta RC, Gupta PL, Gupta RD (1998) Modeling failure time data by lehman alternatives. Commun Stat Theory Methods 27(4): 887–904 · Zbl 0900.62534
[8] Kerridge DF (1961) Inaccuracy and inference. J R Stat Soc Ser B 23: 184–194 · Zbl 0112.10302
[9] Kullback S (1959) Information Theory and Statistics. Wiley, New York · Zbl 0088.10406
[10] Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27: 379–423 · Zbl 1154.94303
[11] Taneja HC, Kumar V, Srivastava R (2009) A dynamic measure of inaccuracy between two residual lifetime distributions. Int Math Fourm 4(25): 1213–1220 · Zbl 1185.62032
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.