General proportional mean residual life model

Mohamed Kayid; Salman Izadkhah; Dalal ALmufarrej

Applications of Mathematics (2016)

  • Volume: 61, Issue: 5, page 607-622
  • ISSN: 0862-7940

Abstract

top
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.

How to cite

top

Kayid, Mohamed, Izadkhah, Salman, and ALmufarrej, Dalal. "General proportional mean residual life model." Applications of Mathematics 61.5 (2016): 607-622. <http://eudml.org/doc/286834>.

@article{Kayid2016,
abstract = {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.},
author = {Kayid, Mohamed, Izadkhah, Salman, ALmufarrej, Dalal},
journal = {Applications of Mathematics},
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)},
language = {eng},
number = {5},
pages = {607-622},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {General proportional mean residual life model},
url = {http://eudml.org/doc/286834},
volume = {61},
year = {2016},
}

TY - JOUR
AU - Kayid, Mohamed
AU - Izadkhah, Salman
AU - ALmufarrej, Dalal
TI - General proportional mean residual life model
JO - Applications of Mathematics
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 5
SP - 607
EP - 622
AB - 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.
LA - eng
KW - 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)
UR - http://eudml.org/doc/286834
ER -

References

top
  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). (1975) Zbl0379.62080MR0438625
  2. Behboodian, J., 10.1080/0020739940250503, Int. J. Math. Educ. Sci. Technol. 25 (1994), 643-647. (1994) Zbl0822.60015MR1295325DOI10.1080/0020739940250503
  3. Chen, Y. Q., Cheng, S., Semiparametric regression analysis of mean residual life with censored survival data, Biometrika 92 (2005), 19-29. (2005) Zbl1068.62044MR2158607
  4. Chen, Y. Q., Jewell, N. P., Lei, X., Cheng, S. C., 10.1111/j.0006-341X.2005.030224.x, Biometrics 61 (2005), 170-178. (2005) Zbl1077.62079MR2135857DOI10.1111/j.0006-341X.2005.030224.x
  5. Gupta, R. C., 10.1017/S0269964815000388, Probab. Eng. Inf. Sci. 30 (2016), 281-297. (2016) Zbl1373.62496MR3478846DOI10.1017/S0269964815000388
  6. Gupta, R. C., Kirmani, S. N. U. A., 10.1080/02331889808802660, Statistics 32 (1998), 175-187. (1998) Zbl0916.62064MR1708121DOI10.1080/02331889808802660
  7. Karlin, S., Total Positivity. Vol. I, Stanford University Press, Stanford (1968). (1968) MR0230102
  8. Kayid, M., Izadkhah, S., 10.1016/j.orl.2015.01.011, Oper. Res. Lett. 43 (2015), 183-188. (2015) MR3319482DOI10.1016/j.orl.2015.01.011
  9. Kayid, M., Izadkhah, S., ALmufarrej, D., 10.1109/TR.2015.2491600, IEEE Trans. Reliab. 65 (2016), 860-866. (2016) DOI10.1109/TR.2015.2491600
  10. Lai, C.-D., Xie, M., Stochastic Ageing and Dependence for Reliability, Springer, New York (2006). (2006) Zbl1098.62130MR2223811
  11. Maguluri, G., Zhang, C.-H., Estimation in the mean residual life regression model, J. R. Stat. Soc., Ser. B 56 (1994), 477-489. (1994) Zbl0803.62083MR1278221
  12. Mansourvar, Z., Martinussen, T., Scheike, T. H., 10.1080/02664763.2015.1043871, J. Appl. Stat. 42 (2015), 2597-2613. (2015) MR3428833DOI10.1080/02664763.2015.1043871
  13. Nanda, A. K., Bhattacharjee, S., Alam, S. S., 10.1016/j.spl.2005.10.019, Stat. Probab. Lett. 76 (2006), 880-890. (2006) Zbl1089.62120MR2268431DOI10.1016/j.spl.2005.10.019
  14. Nanda, A. K., Bhattacharjee, S., Balakrishnan, N., 10.1109/TR.2009.2035791, IEEE Trans. Reliab. 59 (2010), 55-65. (2010) DOI10.1109/TR.2009.2035791
  15. Nanda, A. K., Das, S., Balakrishnan, N., 10.1017/S0269964813000259, Probab. Eng. Inf. Sci. 27 (2013), 553-588. (2013) Zbl1282.90058MR3150113DOI10.1017/S0269964813000259
  16. Nelsen, R. B., An Introduction to Copulas, Springer Series in Statistics Springer, New York (2006). (2006) Zbl1152.62030MR2197664
  17. Oakes, D., Dasu, T., 10.1214/lnms/1215092393, Crossing Boundaries: Statistical Essays in Honor of J. Hall IMS Lecture Notes Monogr. Ser. 43 Inst. Math. Statist., Beachwood (2003), 105-116. (2003) Zbl1255.62314MR2125050DOI10.1214/lnms/1215092393
  18. Shaked, M., Shanthikumar, J. G., Stochastic Orders, Springer Series in Statistics Springer, New York (2007). (2007) MR2265633
  19. Zahedi, H., 10.1016/0378-3758(92)90135-F, J. Stat. Plann. Inference 29 (1991), 221-228. (1991) MR1133703DOI10.1016/0378-3758(92)90135-F
  20. Zhao, W., Elsayed, E. A., 10.1080/00207720500160084, Int. J. Syst. Sci. 36 (2005), 689-696. (2005) Zbl1087.90020MR2171201DOI10.1080/00207720500160084

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.