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On length biased dynamic measure of past inaccuracy. (English) Zbl 1241.62014
Summary: In this communication we introduce a length biased past inaccuracy measure between two past life time distributions over the interval \((0,\,t)\). Based on the proportional reversed hazard model the characterization problem for the length biased inaccuracy measure has been studied. An upper bound to the weighted past inaccuracy measure has also been derived, which reduces to the upper bound obtained in case of weighted past entropy.

62E10 Characterization and structure theory of statistical distributions
62B10 Statistical aspects of information-theoretic topics
62N99 Survival analysis and censored data
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[1] Belis M, Guiasu S (1968) A qualitative measure of information in cybernatic systems. IEEE Trans Inf Theory 4: 593–594
[2] Cox DR (1959) The analysis of exponentially distributed lifetimes with two tpye of failure. J Roy Statist Soc Ser B 21: 411–421 · Zbl 0093.15704
[3] Di Crescenzo A (2000) Some results on the proportional reversed hazards model. Stat Prob Lett 50: 313–321 · Zbl 0967.60016
[4] Di Crescenzo A, Longobardi M (2002) Entropy-based measure of uncertainty in past lifetime distributions. J Appl Probab 39: 434–440 · Zbl 1003.62087
[5] Di Crescenzo A, Longobardi M (2004) A measure of discrimination between past lifetime distributions. Statis Probab Lett 67: 173–182 · Zbl 1058.62088
[6] Di Crescenzo A, Longobardi M (2006) On weighted residual and past entropies. Sci Math Japonicae 64: 255–266 · Zbl 1106.62114
[7] Ebrahimi N (1996) How to measure uncertainty about residual lifetime. Sankhya Ser A 58: 48–57 · Zbl 0893.62098
[8] Ebrahimi N, Pellerey F (1995) New partial ordering of survival functions based on notation of uncertainty. J Appl Prob 32: 202–211 · Zbl 0817.62082
[9] Ebrahimi N, Kirmani SNUA (1996a) A measure of discrimination between two residual life-time distributions and its applications. Ann Inst Statist Math 48(2): 257–265 · Zbl 0861.62063
[10] 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
[11] Gupta RC, Gupta PL, Gupta RD (1998) Modeling failure time data by lehman alternatives. Comm Statist-Theory Methods 27(4): 887–904 · Zbl 0900.62534
[12] Gupta RC, Gupta RD (2007) Proportional reversed hazards models and its applications. J Stat Plan Infer 137: 3525–3536 · Zbl 1119.62098
[13] Kerridge DF (1961) Inaccuracy and inference. J Roy Statist Soc Ser B 23: 184–194 · Zbl 0112.10302
[14] Kullback S (1959) Information theory and statistics. Wiley, New York · Zbl 0088.10406
[15] Kumar V, Taneja HC, Srivastava R (2009) A dynamic measure of inaccuracy between two past lifetime distributions.(to appear in MERTIKA) · Zbl 1185.62032
[16] Rao CR (1965) On discrete distributions arising out of methods of ascertainment. In: Patil GP (eds) Classical and contagious discrete distributions. Pergamon Press and Statistical Publishing Society, Calcutta, pp 320–332
[17] Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27: 379–423 · Zbl 1154.94303
[18] 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
[19] Taneja HC, Tuteja RK (1984) Characterization of a quantitative-qualitative of relative information. Inf Sci 33: 217–222 · Zbl 0558.94003
[20] Taneja HC, Tuteja RK (1986) Characterization of a quantitative-qualitative measure of inaccuracy. Kybernetika 22: 393–402 · Zbl 0622.94008
[21] Taneja HC (1985) On measures of relative ’useful’ information. Kybernetika 21(2): 148–156 · Zbl 0574.94009
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