Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
stochastic order; preservation property; decreasing failure rate (DFR); increasing mean residual life (IMRL)
stochastic order; preservation property; decreasing failure rate (DFR); increasing mean residual life (IMRL)
Summary:
By considering a covariate random variable in the ordinary proportional mean residual life (PMRL) model, we introduce and study a general model, taking more situations into account with respect to the ordinary PMRL model. We investigate how stochastic structures of the proposed model are affected by the stochastic properties of the baseline and the mixing variables in the model. Several characterizations and preservation properties of the new model under different stochastic orders and aging classes are provided. In addition, to illustrate different properties of the model, some examples are presented.
References:
[1] 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
[2] Behboodian, J.: Covariance inequality and its applications. Int. J. Math. Educ. Sci. Technol. 25 (1994), 643-647. DOI 10.1080/0020739940250503 | MR 1295325 | Zbl 0822.60015
[3] Chen, Y. Q., Cheng, S.: Semiparametric regression analysis of mean residual life with censored survival data. Biometrika 92 (2005), 19-29. MR 2158607 | Zbl 1068.62044
[4] Chen, Y. Q., Jewell, N. P., Lei, X., Cheng, S. C.: Semiparametric estimation of proportional mean residual life model in presence of censoring. Biometrics 61 (2005), 170-178. DOI 10.1111/j.0006-341X.2005.030224.x | MR 2135857 | Zbl 1077.62079
[5] Gupta, R. C.: Mean residual life function for additive and multiplicative hazard rate models. Probab. Eng. Inf. Sci. 30 (2016), 281-297. DOI 10.1017/S0269964815000388 | MR 3478846 | Zbl 1373.62496
[6] Gupta, R. C., Kirmani, S. N. U. A.: On the proportional mean residual life model and its implications. Statistics 32 (1998), 175-187. DOI 10.1080/02331889808802660 | MR 1708121 | Zbl 0916.62064
[7] Karlin, S.: Total Positivity. Vol. I. Stanford University Press, Stanford (1968). MR 0230102
[8] Kayid, M., Izadkhah, S.: A new extended mixture model of residual lifetime distributions. Oper. Res. Lett. 43 (2015), 183-188. DOI 10.1016/j.orl.2015.01.011 | MR 3319482
[9] Kayid, M., Izadkhah, S., ALmufarrej, D.: Random effect additive mean residual life model. IEEE Trans. Reliab. 65 (2016), 860-866. DOI 10.1109/TR.2015.2491600
[10] Lai, C.-D., Xie, M.: Stochastic Ageing and Dependence for Reliability. Springer, New York (2006). MR 2223811 | Zbl 1098.62130
[11] Maguluri, G., Zhang, C.-H.: Estimation in the mean residual life regression model. J. R. Stat. Soc., Ser. B 56 (1994), 477-489. MR 1278221 | Zbl 0803.62083
[12] Mansourvar, Z., Martinussen, T., Scheike, T. H.: Semiparametric regression for restricted mean residual life under right censoring. J. Appl. Stat. 42 (2015), 2597-2613. DOI 10.1080/02664763.2015.1043871 | MR 3428833
[13] Nanda, A. K., Bhattacharjee, S., Alam, S. S.: Properties of proportional mean residual life model. Stat. Probab. Lett. 76 (2006), 880-890. DOI 10.1016/j.spl.2005.10.019 | MR 2268431 | Zbl 1089.62120
[14] Nanda, A. K., Bhattacharjee, S., Balakrishnan, N.: Mean residual life function, associated orderings and properties. IEEE Trans. Reliab. 59 (2010), 55-65. DOI 10.1109/TR.2009.2035791
[15] Nanda, A. K., Das, S., Balakrishnan, N.: On dynamic proportional mean residual life model. Probab. Eng. Inf. Sci. 27 (2013), 553-588. DOI 10.1017/S0269964813000259 | MR 3150113 | Zbl 1282.90058
[16] Nelsen, R. B.: An Introduction to Copulas. Springer Series in Statistics Springer, New York (2006). MR 2197664 | Zbl 1152.62030
[17] Oakes, D., Dasu, T.: Inference for the proportional mean residual life model. Crossing Boundaries: Statistical Essays in Honor of J. Hall IMS Lecture Notes Monogr. Ser. 43 Inst. Math. Statist., Beachwood (2003), 105-116. DOI 10.1214/lnms/1215092393 | MR 2125050 | Zbl 1255.62314
[18] Shaked, M., Shanthikumar, J. G.: Stochastic Orders. Springer Series in Statistics Springer, New York (2007). MR 2265633
[19] Zahedi, H.: Proportional mean remaining life model. J. Stat. Plann. Inference 29 (1991), 221-228. DOI 10.1016/0378-3758(92)90135-F | MR 1133703
[20] Zhao, W., Elsayed, E. A.: Modelling accelerated life testing based on mean residual life. Int. J. Syst. Sci. 36 (2005), 689-696. DOI 10.1080/00207720500160084 | MR 2171201 | Zbl 1087.90020
Search
Partner of
