Asha, G.; Elbatal, I.; Rejeesh, C. J. Further results on discrete mean past lifetime. (English) Zbl 1338.60047 Commun. Stat., Theory Methods 45, No. 4, 1081-1098 (2016). Summary: The present paper aims at studying the mean past lifetime of a discrete random variable. The notion of discrete mean past lifetime is studied in relation to the concepts of reversed hazard rate, reversed lack of memory property, and cumulative past entropy. New classes of distributions characterized by particular forms of discrete mean past life are also investigated. Implications of an increasing mean past lifetime on other reliability notions are studied and finally some bivariate generalizations are discussed. Cited in 1 Document MSC: 60E15 Inequalities; stochastic orderings 62E10 Characterization and structure theory of statistical distributions 62N05 Reliability and life testing Keywords:characterizations; discrete mean past lifetime; past entropy; reversed lack of memory; stochastic ordering PDFBibTeX XMLCite \textit{G. Asha} et al., Commun. Stat., Theory Methods 45, No. 4, 1081--1098 (2016; Zbl 1338.60047) Full Text: DOI References: [1] Asha G., Calcutta Stat. Assoc. Bull. 65 (233) pp 1– (2007) · Zbl 1147.62304 · doi:10.1177/0008068320070101 [2] DOI: 10.1016/j.spl.2009.03.014 · Zbl 1167.62012 · doi:10.1016/j.spl.2009.03.014 [3] Barlow R. E., Statistical theory of reliability and life testing probability models (1975) · Zbl 0379.62080 [4] Bebbington M., Advanced Reliability Modelling IV: Beyond the Traditional Reliability and Maintainability Approaches, Proceedings 4th Asia-Pacific Symposium (APARM 2010) pp 57– (2010) [5] Bismi, G. (2005). Bivariate burr distributions. Ph.D. Thesis. Cochin University of Science and Technology, Dhyuthi, India. Unpublished. · Zbl 1134.62311 [6] DOI: 10.1142/S0218539303001007 · doi:10.1142/S0218539303001007 [7] Dewan, I., Sudheesh, K.K. (2009). On proportional (reversed) hazard model for discrete data. Technical report. Indian Statistical Institute, New Delhi, India. [8] Dewan I., Proceedings of the IEEE International Conference on Quality and Reliability (2011) [9] DOI: 10.1016/j.jspi.2009.05.038 · Zbl 1172.94543 · doi:10.1016/j.jspi.2009.05.038 [10] DOI: 10.1007/s00184-007-0153-4 · Zbl 1433.62291 · doi:10.1007/s00184-007-0153-4 [11] DOI: 10.1016/S0378-3758(97)00064-5 · Zbl 0908.62099 · doi:10.1016/S0378-3758(97)00064-5 [12] DOI: 10.1016/j.ress.2010.04.009 · doi:10.1016/j.ress.2010.04.009 [13] DOI: 10.1080/03610926.2010.535626 · Zbl 1301.62102 · doi:10.1080/03610926.2010.535626 [14] DOI: 10.1016/j.jspi.2009.11.011 · Zbl 1186.60012 · doi:10.1016/j.jspi.2009.11.011 [15] Lai C.D., Qual. Technol. Quant. Manag. 10 (2) pp 251– (2013) · doi:10.1080/16843703.2013.11673320 [16] DOI: 10.1017/S0269964806060293 · Zbl 1122.60018 · doi:10.1017/S0269964806060293 [17] DOI: 10.1006/jmva.1997.1682 · Zbl 0890.62040 · doi:10.1006/jmva.1997.1682 [18] Nair N.U., J. Indian Soc. Probab. Stat. 8 pp 45– (2004) [19] Nanda A.K., Sankhya Ser. A. 67 (1) pp 106– (2005) [20] DOI: 10.1016/0026-2714(92)90015-D · doi:10.1016/0026-2714(92)90015-D [21] DOI: 10.1109/24.536985 · Zbl 04534005 · doi:10.1109/24.536985 [22] DOI: 10.1109/TR.1982.5221432 · Zbl 0507.62084 · doi:10.1109/TR.1982.5221432 [23] Shaked M., Stochastic Orders and Their Applications (1994) · Zbl 0806.62009 [24] Shaked M., Stat. Sin. 4 pp 567– (1994) [25] DOI: 10.1016/0305-0548(94)00048-D · Zbl 0822.90073 · doi:10.1016/0305-0548(94)00048-D [26] DOI: 10.1002/j.1538-7305.1948.tb01338.x · Zbl 1154.94303 · doi:10.1002/j.1538-7305.1948.tb01338.x [27] DOI: 10.1080/03610928308828617 · Zbl 0552.62008 · doi:10.1080/03610928308828617 [28] DOI: 10.1142/S0218539302000822 · doi:10.1142/S0218539302000822 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.