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GENERALIZATION OF THE PAIRWISE STOCHASTIC PRECEDENCE ORDER TO THE SEQUENCE OF RANDOM VARIABLES

Published online by Cambridge University Press:  18 March 2020

Maxim Finkelstein Open the ORCID record for Maxim Finkelstein [Opens in a new window]  and
Nil Kamal Hazra
Maxim Finkelstein
Affiliation:
Department of Mathematical Statistics and Actuarial Science, University of the Free State, 339 Bloemfontein 9300, South Africa; ITMO University, Saint Petersburg, Russia E-mail: finkelm@ufs.ac.za
Nil Kamal Hazra
Affiliation:
Department of Mathematics, Indian Institute of Technology Jodhpur, Karwar 342037, India
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Abstract

We discuss a new stochastic ordering for the sequence of independent random variables. It generalizes the stochastic precedence (SP) order that is defined for two random variables to the case n > 2. All conventional stochastic orders are transitive, whereas the SP order is not. Therefore, a new approach to compare the sequence of random variables had to be developed that resulted in the notion of the sequential precedence order. A sufficient condition for this order is derived and some examples are considered.

Keywords

hazard rate orderlikelihood ratio ordernontransitivitystochastic precedence orderusual stochastic order
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 3 , July 2021 , pp. 699 - 707
Copyright
© Cambridge University Press 2020

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References

1.Arcones, M.A., Kvam, P.H., & Samaniego, F.J. (2002). Nonparametric estimation of a distribution subject to a stochastic precedence constraint. Journal of American Statistical Association 97: 170–182.CrossRefGoogle Scholar
2.Barlow, R.E. & Proschan, F. (1975). Statistical theory of reliability and life testing. New York: Holt, Renerhart and Winston.Google Scholar
3.Blyth, C.R. (1972). Some probability paradoxes in choice from among random alternatives. Journal of American Statistical Association 67: 366–373.Google Scholar
4.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
5.Finkelstein, M. (2013). On some comparisons of lifetimes for reliability analysis. Reliability Engineering and System Safety 119: 300–304.CrossRefGoogle Scholar
6.Finkelstein, M. & Cha, J.H. (2013). Stochastic modelling for reliability: shocks, burn-in, and heterogeneous populations. London: Springer.Google Scholar
7.Hollander, M. & Samaniego, F.J. (2008). The use of stochastic precedence in the comparison of engineered systems. In Bedford, T., Quigley, J., Walls, L., Alkali, B., Daneshkhah, A. & Hardman, G. (eds), Advances in mathematical modeling for reliability. Amsterdam: IOS Press, pp. 129–137.Google Scholar
8.Montes, I. & Montes, S. (2016). Stochastic dominance and statistical preference for random variables couple by an Archimedean copula or by the Frèchet-Hoeffding upper bound. Journal of Multivariate Analysis 143: 275–298.CrossRefGoogle Scholar
9.Navarro, J. & Rubio, R. (2010). Comparisons of coherent systems using stochastic precedence. TEST 19: 469–486.CrossRefGoogle Scholar
10.Samaniego, F.J. (2007). System signatures and their applications in engineering reliability. In International Series in Operations Research and Management Science, vol. 110. New York: Springer.Google Scholar
11.Santis, E.D., Fantozzi, F., & Spizzichino, F. (2015). Relations between stochastic orderings and generalized stochastic precedence. Probability in the Engineering and Informational Sciences 29: 329–343.CrossRefGoogle Scholar
12.Savage, L.J. (1954). The foundations of statistics. New York: John Wiley and Sons.Google Scholar
13.Shaked, M. & Shanthikumar, J.G. (2007). Stochastic orders. New York: Springer.CrossRefGoogle Scholar
14.Zhai, Q., Yang, J., Peng, R., & Zhao, Y. (2015). A study of optimal component order in a general 1-out-of-n warm standby system. IEEE Transactions on Reliability 64: 349–358.CrossRefGoogle Scholar