| Title:
|
On preservation under univariate weighted distributions (English) |
| Author:
|
Izadkhah, Salman |
| Author:
|
Amini, Mohammad |
| Author:
|
Mohtashami Borzadaran, Gholam Reza |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
60 |
| Issue:
|
4 |
| Year:
|
2015 |
| Pages:
|
453-467 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
weighted distribution |
| Keyword:
|
preservation |
| Keyword:
|
stochastic ordering |
| Keyword:
|
aging classes |
| MSC:
|
60E05 |
| MSC:
|
60E15 |
| MSC:
|
62N05 |
| idZBL:
|
Zbl 06486920 |
| idMR:
|
MR3396474 |
| DOI:
|
10.1007/s10492-015-0105-7 |
| . |
| Date available:
|
2015-06-30T12:08:54Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144317 |
| . |
| Reference:
|
[1] Ahmad, I., Kayid, M.: Reversed preservation of stochastic orders for random minima and maxima with applications.Stat. Pap. 48 (2007), 283-293. Zbl 1114.60017, MR 2295816, 10.1007/s00362-006-0331-x |
| Reference:
|
[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). Zbl 0379.62080, MR 0438625 |
| Reference:
|
[3] Bartoszewicz, J.: On a representation of weighted distributions.Stat. Probab. Lett. 79 (2009), 1690-1694. Zbl 1170.60009, MR 2547939, 10.1016/j.spl.2009.04.007 |
| Reference:
|
[4] Bartoszewicz, J., Skolimowska, M.: Preservation of classes of life distributions and stochastic orders under weighting.Stat. Probab. Lett. 76 (2006), 587-596. Zbl 1088.62017, MR 2255787, 10.1016/j.spl.2005.09.003 |
| Reference:
|
[5] Błażej, P.: Preservation of classes of life distributions under weighting with a general weight function.Stat. Probab. Lett. 78 (2008), 3056-3061. Zbl 1158.62010, MR 2474397, 10.1016/j.spl.2008.05.028 |
| Reference:
|
[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. MR 3045360, 10.1080/03610926.2011.598998 |
| Reference:
|
[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. MR 3028980, 10.1080/03610926.2011.586484 |
| Reference:
|
[8] Jain, K., Singh, H., Bagai, I.: Relations for reliability measures of weighted distributions.Commun. Stat., Theory Methods 18 (1989), 4393-4412. Zbl 0707.62197, MR 1046715, 10.1080/03610928908830162 |
| Reference:
|
[9] Karlin, S.: Total Positivity. Vol. I.Stanford University Press, Stanford, California (1968). MR 0230102 |
| Reference:
|
[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. Zbl 1134.60315, 10.1017/S0269964800000498 |
| Reference:
|
[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. Zbl 1136.62065, MR 2392347, 10.1080/03610920701499506 |
| Reference:
|
[12] Nanda, A. K., Jain, K.: Some weighted distribution results on univariate and bivariate cases.J. Stat. Plann. Inference 77 (1999), 169-180. Zbl 0924.62018, MR 1687954, 10.1016/S0378-3758(98)00190-6 |
| Reference:
|
[13] Nanda, A. K., Singh, H., Misra, N., Paul, P.: Reliability properties of reversed residual lifetime.Commun. Stat., Theory Methods 32 (2003), 2031-2042. Zbl 1156.62360, MR 2002004, 10.1081/STA-120023264 |
| Reference:
|
[14] Navarro, J., Aguila, Y. del, Ruiz, J. M.: Characterizations through reliability measures from weighted distributions.Stat. Pap. 42 (2001), 395-402. MR 1860754, 10.1007/s003620100066 |
| Reference:
|
[15] Pakes, A. G., Navarro, J., Ruiz, J. M., Aguila, Y. del: Characterizations using weighted distributions.J. Stat. Plann. Inference 116 (2003), 389-420. MR 2000091, 10.1016/S0378-3758(02)00357-9 |
| Reference:
|
[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. Zbl 0384.62014, MR 0507202, 10.2307/2530008 |
| Reference:
|
[17] Rao, C. R.: On discrete distributions arising out of methods of ascertainment.Sankhy\=a, Ser. A 27 (1965), 311-324. Zbl 0212.21903, MR 0208736 |
| Reference:
|
[18] Shaked, Shanthikumar, J. G.: Stochastic Orders.Springer Series in Statistics Springer, New York (2007). MR 2265633 |
| . |
