Previous |  Up |  Next

Article

Keywords:
weighted distribution; preservation; stochastic ordering; aging classes
Summary:
We derive some new results for preservation of various stochastic orders and aging classes under weighted distributions. The corresponding reversed preservation properties as straightforward conclusions of the obtained results for the direct preservation properties, are developed. Damage model of Rao, residual lifetime distribution, proportional hazards and proportional reversed hazards models are discussed as special weighted distributions to try some of our results.
References:
[1] Ahmad, I., Kayid, M.: Reversed preservation of stochastic orders for random minima and maxima with applications. Stat. Pap. 48 (2007), 283-293. DOI 10.1007/s00362-006-0331-x | MR 2295816 | Zbl 1114.60017
[2] Barlow, R. E., Proschan, F.: Statistical Theory of Reliability and Life Testing. International Series in Decision Processes Holt, Rinehart and Winston, New York (1975). MR 0438625 | Zbl 0379.62080
[3] Bartoszewicz, J.: On a representation of weighted distributions. Stat. Probab. Lett. 79 (2009), 1690-1694. DOI 10.1016/j.spl.2009.04.007 | MR 2547939 | Zbl 1170.60009
[4] Bartoszewicz, J., Skolimowska, M.: Preservation of classes of life distributions and stochastic orders under weighting. Stat. Probab. Lett. 76 (2006), 587-596. DOI 10.1016/j.spl.2005.09.003 | MR 2255787 | Zbl 1088.62017
[5] Błażej, P.: Preservation of classes of life distributions under weighting with a general weight function. Stat. Probab. Lett. 78 (2008), 3056-3061. DOI 10.1016/j.spl.2008.05.028 | MR 2474397 | Zbl 1158.62010
[6] Izadkhah, S., Rezaei, A. H., Amini, M., Borzadaran, G. R. Mohtashami: A general approach for preservation of some aging classes under weighting. Commun. Stat., Theory Methods 42 (2013), 1899-1909. DOI 10.1080/03610926.2011.598998 | MR 3045360
[7] Izadkhah, S., Roknabadi, A. H. Rezaei, Borzadaran, G. R. Mohtashami: On properties of reversed mean residual life order for weighted distributions. Commun. Stat., Theory Methods 42 (2013), 838-851. DOI 10.1080/03610926.2011.586484 | MR 3028980
[8] Jain, K., Singh, H., Bagai, I.: Relations for reliability measures of weighted distributions. Commun. Stat., Theory Methods 18 (1989), 4393-4412. DOI 10.1080/03610928908830162 | MR 1046715 | Zbl 0707.62197
[9] Karlin, S.: Total Positivity. Vol. I. Stanford University Press, Stanford, California (1968). MR 0230102
[10] Kochar, S. C., Gupta, R. P.: Some results on weighted distributions for positive-valued random variables. Probab. Eng. Inf. Sci. 1 (1987), 417-423. DOI 10.1017/S0269964800000498 | Zbl 1134.60315
[11] Misra, N., Gupta, N., Dhariyal, I. D.: Preservation of some aging properties and stochastic orders by weighted distributions. Commun. Stat., Theory Methods 37 (2008), 627-644. DOI 10.1080/03610920701499506 | MR 2392347 | Zbl 1136.62065
[12] Nanda, A. K., Jain, K.: Some weighted distribution results on univariate and bivariate cases. J. Stat. Plann. Inference 77 (1999), 169-180. DOI 10.1016/S0378-3758(98)00190-6 | MR 1687954 | Zbl 0924.62018
[13] Nanda, A. K., Singh, H., Misra, N., Paul, P.: Reliability properties of reversed residual lifetime. Commun. Stat., Theory Methods 32 (2003), 2031-2042. DOI 10.1081/STA-120023264 | MR 2002004 | Zbl 1156.62360
[14] Navarro, J., Aguila, Y. del, Ruiz, J. M.: Characterizations through reliability measures from weighted distributions. Stat. Pap. 42 (2001), 395-402. DOI 10.1007/s003620100066 | MR 1860754
[15] Pakes, A. G., Navarro, J., Ruiz, J. M., Aguila, Y. del: Characterizations using weighted distributions. J. Stat. Plann. Inference 116 (2003), 389-420. DOI 10.1016/S0378-3758(02)00357-9 | MR 2000091
[16] Patil, G. P., Rao, C. R.: Weighted distributions and size-biased sampling with applications to wildlife populations and human families. Biometrics 34 (1978), 179-189. DOI 10.2307/2530008 | MR 0507202 | Zbl 0384.62014
[17] Rao, C. R.: On discrete distributions arising out of methods of ascertainment. Sankhy\=a, Ser. A 27 (1965), 311-324. MR 0208736 | Zbl 0212.21903
[18] Shaked, Shanthikumar, J. G.: Stochastic Orders. Springer Series in Statistics Springer, New York (2007). MR 2265633
Partner of
EuDML logo