Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-26T01:23:12.211Z Has data issue: false hasContentIssue false
  • English
  • Français

RESIDUAL STOCHASTIC PRECEDENCE ORDER

Published online by Cambridge University Press:  28 January 2020

Amit Kumar Misra ,
Vaishali Gupta Open the ORCID record for Vaishali Gupta [Opens in a new window]  and
Neeraj Misra
Amit Kumar Misra
Affiliation:
Department of Statistics, School of Physical & Decision Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow 226 025, India E-mail: [email protected]
Vaishali Gupta
Affiliation:
Department of Statistics, School of Physical & Decision Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow 226 025, India E-mail: [email protected]
Neeraj Misra
Affiliation:
Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur 208 016, India E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The aim of this paper is to introduce a new stochastic order based on the residual lifetimes of two nonnegative dependent random variables and the stochastic precedence order. We develop some characterizations and preservation properties of this stochastic order. In addition, we study some of its reliability properties and its relation with other existing stochastic orders. One of the possible applications in reliability theory has also been discussed.

Keywords

joint stochastic orderspreservationresidual lifetimeunivariate stochastic orders
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 3 , July 2021 , pp. 496 - 512
Copyright
© Cambridge University Press 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Aly, A.A.E., & Kochar, C.S. (1993). On hazard rate ordering of dependent variables. Advances in Applied Probability 25: 477–482.CrossRefGoogle Scholar
2.Alzaid, A.A., Kim, J.S., & Proschan, F. (1991). Laplace ordering and its applications. Journal of Statistical Planning and Inference 28: 16–130.Google Scholar
3.Arcones, M.A., Kvam, P.H., & Samaniego, F.J. (2002). Nonparametric estimation of a distribution subject to a stochastic precedence constraint. Journal of the American Statistical Association 97: 170–182.CrossRefGoogle Scholar
4.Balakrishnan, N., & Zhao, P. (2011). Hazard rate comparison of parallel systems with heterogeneous gamma components. Journal of Multivariate Analysis 113: 153–160.CrossRefGoogle Scholar
5.Balakrishnan, N., Barmalzan, G., & Kosari, S. (2017). On joint weak reversed hazard rate order under symmetric copulas. Mathematical Methods of Statistics 26: 311–318.CrossRefGoogle Scholar
6.Bartoszewicz, J., & Skolimowska, M. (2006). Preservation of classes of life distributions and stochastic orders under weighting. Statistics and Probability Letters 56: 587–596.Google Scholar
7.Belzunce, F., Ortega, E.M., Pellerey, F., & Ruiz, J.M. (2007). On rankings and top choices in random utility models with dependent utilities. Metrika 66: 197–212.CrossRefGoogle Scholar
8.Belzunce, F., Martínez-Puertas, H., & Ruiz, J.M. (2013). On allocation of redundant components for systems with dependent components. European Journal of Operational Research 230: 573–580.CrossRefGoogle Scholar
9.Belzunce, F., Martínez-Riquelme, C., & Mulero, J. (2016). An introduction to stochastic orders. London, UK: Elsevier-Academic Press.Google Scholar
10.Belzunce, F., Martínez-Riquelme, C., Pellerey, F., & Zalzadeh, S. (2016). Comparison of hazard rates for dependent random variables. Statistics 50: 630–648.CrossRefGoogle Scholar
11.Boland, P.J., Singh, H., & Cukic, B. (2004). The stochastic precedence ordering with applications in sampling and testing. Journal of Applied Probability 41: 73–82.CrossRefGoogle Scholar
12.Cai, N., & Zheng, Y. (2012). Preservation of generalized ageing class on the residual life at random time. Journal of Statistical Planning and Inference 142: 148–154.CrossRefGoogle Scholar
13.Ding, W., Da, G., & Li, X. (2014). Comparisons of series and parallel systems with heterogeneous components. Probability in the Engineering and Informational Sciences 28: 39–53.CrossRefGoogle Scholar
14.Guess, F., & Proschan, F. (1988). Mean residual life: theory and applications. Handbook of Reliability and Statistics: Quality Control and Reliability 7: 215–224.CrossRefGoogle Scholar
15.Gupta, N. (2013). Stochastic comparisons of residual lifetimes and inactivity times of coherent systems. Journal of Applied Probability 50: 848–860.CrossRefGoogle Scholar
16.Gupta, N., Misra, N., & Kumar, S. (2015). Stochastic comparisons of residual lifetimes and inactivity times of coherent systems with dependent identically distributed components. European Journal of Operational Research 240: 425–430.CrossRefGoogle Scholar
17.Hazra, N.K., & Nanda, A.K. (2016). On some generalized orderings: In the spirit of relative ageing. Communications in Statistics – Theory and Methods 45: 6165–6181.Google Scholar
18.Kalashnikov, V.V., & Rachev, S.T. (1986). Characterization of queueing models and their stability estimates. In Prohorov, Yu.K., (eds.), Probability Theory and Mathematical Statistics, vol 2, Amsterdam: VNU Science Press, pp. 37–53.Google Scholar
19.Kayid, M., Izadkhah, S., & Alshami, S (2014). Residual probability function, associated orderings, and related aging classes. Mathematical Problems in Engineering 2, 1–10.Google Scholar
20.Li, H., & Li, X. (2013). Stochastic orders in reliability and risk management. New York: Springer.CrossRefGoogle Scholar
21.Li, X., & You, Y. (2014). A note on allocation of portfolio shares of random assets with archimedean copula. Annals of Operations Research 212: 155–167.CrossRefGoogle Scholar
22.Li, X., & You, Y. (2015). Permutation monotone functions of random vectors with applications in financial and actuarial risk management. Advances in Applied Probability 47: 270–291.CrossRefGoogle Scholar
23.Mi, J. (1999). Optimal active redundancy allocation in k-out-of-n system. Journal of Applied Probability 36: 927–933.CrossRefGoogle Scholar
24.Misra, A.K., & Misra, N. (2011). A note on active redundancy allocations in k-out-of-n systems. Statistics and Probability Letters 81: 1518–1523.CrossRefGoogle Scholar
25.Misra, N., & Misra, A.K. (2012). New results on stochastic comparisons of two-component series and parallel systems. Statistics and Probability Letters 82: 283–290.Google Scholar
26.Misra, N., & Francis, J. (2018). Relative aging of (n − k + 1)-out-of-n systems based on cumulative hazard and cumulative reversed hazard functions. Naval Research Logistics 65: 566–575.CrossRefGoogle Scholar
27.Misra, N., Francis, J., & Naqvi, S. (2017). Some sufficient conditions for relative aging of life distributions. Probability in the Engineering and Informational Sciences 31: 83–99.CrossRefGoogle Scholar
28.Misra, N., Gupta, N., & Dhariyal, I.D. (2008). Preservation of some ageing properties and stochastic orders by weighted distributions. Communications in Statistics – Theory and Methods 37: 627–644.CrossRefGoogle Scholar
29.Misra, N., Misra, A.K., & Dhariyal, I.D. (2011). Active redundancy allocations in series systems. Probability in the Engineering and Informational Sciences 25: 219–235.CrossRefGoogle Scholar
30.Müller, A., & Stoyan, D (2002). Comparison methods for stochastic models and risks. Wiley Series in Probability and Statistics. Chichester, England: John Wiley and Sons, Ltd.Google Scholar
31.Nanda, A.K., & Shaked, M. (2001). The hazard rate and reversed hazard rate orders, with applications to order statistics. The Institute of Statistical Mathematics 53: 853–864.CrossRefGoogle Scholar
32.Nanda, A.K., Bhattacharjee, S., & Balakrishnan, N. (2010). Mean residual life function, associated orderings and properties. IEEE Transactions on Reliability 59: 55–65.Google Scholar
33.Pellerey, F., & Zalzadeh, S. (2015). A note on relationships between some univariate stochastic orders and the corresponding joint stochastic orders. Metrika 78: 399–414.CrossRefGoogle Scholar
34.Pellerey, F., & Spizzichino, F. (2016). Joint weak hazard rate order under non-symmetric copulas. Dependence Modeling 4: 190–204.CrossRefGoogle Scholar
35.Sengupta, D., & Deshpande, J.V. (1994). Some results on the relative ageing of two life distributions. Journal of Applied Probability 31: 991–1003.CrossRefGoogle Scholar
36.Shaked, M., & Shanthikumar, J.G. (2007). Stochastic orders. New York: Springer.CrossRefGoogle Scholar
37.Shanthikumar, J.G., & Yao, D.D. (1991). Bivariate characterization of some stochastic order relations. Advances in Applied Probability 23: 642–659.CrossRefGoogle Scholar
38.Singh, H., & Misra, N. (1994). On redundancy allocations in systems. Journal of Applied Probability 31: 1004–1014.CrossRefGoogle Scholar
39.Valdés, J.E., Arango, G., Zequeira, R.I., & Brito, G. (2010). Some stochastic comparisons in series systems with active redundancy. Statistics and Probability Letters 80: 945–949.CrossRefGoogle Scholar
40.Zardasht, V., & Asadi, M. (2010). Evaluation of P(X t > Y t) when both X t and Y t are residual lifetimes of two systems. Statistica Neerlandica 64: 460–481.CrossRefGoogle Scholar