Some stochastic comparison results for series and parallel systems with heterogeneous Pareto type components

Lakshmi Kanta Patra; Suchandan Kayal; Phalguni Nanda

Applications of Mathematics (2018)

  • Volume: 63, Issue: 1, page 55-77
  • ISSN: 0862-7940

Abstract

top
We focus on stochastic comparisons of lifetimes of series and parallel systems consisting of independent and heterogeneous new Pareto type components. Sufficient conditions involving majorization type partial orders are provided to obtain stochastic comparisons in terms of various magnitude and dispersive orderings which include usual stochastic order, hazard rate order, dispersive order and right spread order. The usual stochastic order of lifetimes of series systems with possibly different scale and shape parameters is studied when its matrix of parameters changes to another matrix in certain sense.

How to cite

top

Patra, Lakshmi Kanta, Kayal, Suchandan, and Nanda, Phalguni. "Some stochastic comparison results for series and parallel systems with heterogeneous Pareto type components." Applications of Mathematics 63.1 (2018): 55-77. <http://eudml.org/doc/294518>.

@article{Patra2018,
abstract = {We focus on stochastic comparisons of lifetimes of series and parallel systems consisting of independent and heterogeneous new Pareto type components. Sufficient conditions involving majorization type partial orders are provided to obtain stochastic comparisons in terms of various magnitude and dispersive orderings which include usual stochastic order, hazard rate order, dispersive order and right spread order. The usual stochastic order of lifetimes of series systems with possibly different scale and shape parameters is studied when its matrix of parameters changes to another matrix in certain sense.},
author = {Patra, Lakshmi Kanta, Kayal, Suchandan, Nanda, Phalguni},
journal = {Applications of Mathematics},
keywords = {stochastic order; parallel system; series system; majorization; multivariate chain majorization; Pareto type distribution; $T$-transform matrix},
language = {eng},
number = {1},
pages = {55-77},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some stochastic comparison results for series and parallel systems with heterogeneous Pareto type components},
url = {http://eudml.org/doc/294518},
volume = {63},
year = {2018},
}

TY - JOUR
AU - Patra, Lakshmi Kanta
AU - Kayal, Suchandan
AU - Nanda, Phalguni
TI - Some stochastic comparison results for series and parallel systems with heterogeneous Pareto type components
JO - Applications of Mathematics
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 1
SP - 55
EP - 77
AB - We focus on stochastic comparisons of lifetimes of series and parallel systems consisting of independent and heterogeneous new Pareto type components. Sufficient conditions involving majorization type partial orders are provided to obtain stochastic comparisons in terms of various magnitude and dispersive orderings which include usual stochastic order, hazard rate order, dispersive order and right spread order. The usual stochastic order of lifetimes of series systems with possibly different scale and shape parameters is studied when its matrix of parameters changes to another matrix in certain sense.
LA - eng
KW - stochastic order; parallel system; series system; majorization; multivariate chain majorization; Pareto type distribution; $T$-transform matrix
UR - http://eudml.org/doc/294518
ER -

References

top
  1. Arnold, B. C., 10.1214/0883423060000000097, Stat. Sci. 22 (2007), 407-413. (2007) Zbl1246.01010MR2416816DOI10.1214/0883423060000000097
  2. Balakrishnan, N., Haidari, A., Masoumifard, K., 10.1109/tr.2014.2354192, IEEE Trans. Reliab. 64 (2015), 333-348. (2015) DOI10.1109/tr.2014.2354192
  3. Balakrishnan, N., (eds.), C. R. Rao, 10.1016/S0169-7161(98)17001-3, Handbook of Statistics 17, North-Holland, Amsterdam (1998). (1998) Zbl0897.00016MR1672283DOI10.1016/S0169-7161(98)17001-3
  4. Balakrishnan, N., Zhao, P., 10.1016/j.jmva.2011.05.001, J. Multivariate Anal. 113 (2013), 153-160. (2013) Zbl1253.60022MR2984362DOI10.1016/j.jmva.2011.05.001
  5. Barmalzan, G., Najafabadi, A. T. Payandeh, Balakrishnan, N., 10.1016/j.spl.2015.11.009, Stat. Probab. Lett. 110 (2016), 1-7. (2016) Zbl06572266MR3474731DOI10.1016/j.spl.2015.11.009
  6. Bourguignon, M., Saulo, H., Fernandez, R. Nobre, 10.1016/j.physa.2016.03.043, Physica A: Statistical Mechanics and its Applications 457 (2016), 166-175. (2016) MR3493327DOI10.1016/j.physa.2016.03.043
  7. David, H. A., Nagaraja, H. N., 10.1002/0471722162, Wiley Series in Probability and Statistics, John Wiley & Sons, Chichester (2003). (2003) Zbl1053.62060MR1994955DOI10.1002/0471722162
  8. Dykstra, R., Kochar, S., Rojo, J., 10.1016/S0378-3758(97)00058-X, J. Stat. Plann. Inference 65 (1997), 203-211. (1997) Zbl0915.62044MR1622774DOI10.1016/S0378-3758(97)00058-X
  9. Fang, L., Balakrishnan, N., 10.1007/s00184-015-0573-5, Metrika 79 (2016), 693-703. (2016) Zbl1373.62494MR3518582DOI10.1007/s00184-015-0573-5
  10. Fang, L., Balakrishnan, N., 10.1080/02331888.2016.1142545, Statistics 50 (2016), 1195-1205. (2016) Zbl06673721MR3552988DOI10.1080/02331888.2016.1142545
  11. Fang, L., Wang, Y., 10.3390/sym9010010, Symmetry 9 (2017), Paper No. 10, 9 pages. (2017) MR3618925DOI10.3390/sym9010010
  12. Fang, L., Zhang, X., 10.1016/j.jkss.2011.05.004, J. Korean Stat. Soc. 41 13-16 (2012). (2012) Zbl1296.62106MR2933211DOI10.1016/j.jkss.2011.05.004
  13. Fang, L., Zhang, X., 10.1016/j.spl.2014.10.017, Stat. Probab. Lett. 97 (2015), 25-31. (2015) Zbl1314.60063MR3299747DOI10.1016/j.spl.2014.10.017
  14. Fang, L., Zhu, X., Balakrishnan, N., 10.1016/j.spl.2016.01.021, Stat. Probab. Lett. 112 131-136 (2016). (2016) Zbl1338.60051MR3475497DOI10.1016/j.spl.2016.01.021
  15. Gupta, N., Patra, L. K., Kumar, S., 10.1016/j.orl.2015.09.009, Oper. Res. Lett. 43 612-615 (2015). (2015) MR3423556DOI10.1016/j.orl.2015.09.009
  16. Hardy, G. H., Littlewood, J. E., Polya, G., Inequalities, University Press, Cambridge (1934). (1934) Zbl0010.10703MR0944909
  17. Khaledi, B.-E., Farsinezhad, S., Kochar, S. C., 10.1016/j.jspi.2010.06.006, J. Stat. Plann. Inference 141 (2011), 276-286. (2011) Zbl1207.62108MR2719493DOI10.1016/j.jspi.2010.06.006
  18. Khaledi, B.-E., Kochar, S., 10.1080/03610920601077212, Commun. Stat., Theory Methods 36 (2007), 1441-1449. (2007) Zbl1119.60013MR2405269DOI10.1080/03610920601077212
  19. Marshall, A. W., Olkin, I., 10.1016/c2009-0-22048-4, Mathematics in Science and Engineering 143, Academic Press, New York (1979). (1979) Zbl0437.26007MR0552278DOI10.1016/c2009-0-22048-4
  20. Nadarajah, S., Jiang, X., Chu, J., 10.1007/s10479-017-2444-0, Ann. Oper. Res. 254 191-209 (2017). (2017) Zbl06764423MR3665743DOI10.1007/s10479-017-2444-0
  21. Pečarić, J. E., Proschan, F., Tong, Y. L., 10.1016/s0076-5392(08)x6162-4, Mathematics in Science and Engineering 187, Academic Press, Boston (1992). (1992) Zbl0749.26004MR1162312DOI10.1016/s0076-5392(08)x6162-4
  22. Shaked, M., Shanthikumar, J. G., 10.1007/978-0-387-34675-5, Springer Series in Statistics, New York (2007). (2007) Zbl1111.62016MR2265633DOI10.1007/978-0-387-34675-5
  23. Zhao, P., Balakrishnan, N., 10.1007/s00184-010-0297-5, Metrika 74 203-210 (2011). (2011) Zbl05963332MR2822156DOI10.1007/s00184-010-0297-5

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.