Hostname: page-component-8448b6f56d-xtgtn Total loading time: 0 Render date: 2024-04-23T08:12:40.552Z Has data issue: false hasContentIssue false
  • English
  • Français

Mean residual life order among largest order statistics arising from resilience-scale models with reduced scale parameters

Published online by Cambridge University Press:  22 November 2022

Abedin Haidari ,
Mostafa Sattari  and
Ghobad Barmalzan Open the ORCID record for Ghobad Barmalzan [Opens in a new window]
Abedin Haidari
Affiliation:
Department of Mathematics Faculty of Basic Science, Ilam University, Ilam, Iran
Mostafa Sattari
Affiliation:
Department of Mathematics, University of Zabol, Sistan and Baluchestan, Iran
Ghobad Barmalzan
Affiliation:
Department of Basic Science, Kermanshah University of Technology, Kermanshah, Iran. E-mail: gh.saadatkia@kut.ac.ir
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we identify some conditions to compare the largest order statistics from resilience-scale models with reduced scale parameters in the sense of mean residual life order. As an example of the established result, the exponentiated generalized gamma distribution is examined. Also, for the special case of the scale model, power-generalized Weibull and half-normal distributions are investigated.

Keywords

Exponentiated generalized gamma distributionHalf-normal distributionMean residual life orderPower-generalized Weibull distributionReciprocal majorization orderResilience-scale model
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 37 , Issue 1 , January 2023 , pp. 72 - 85
Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press

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

AL-Hussaini, E.K. & Ahsanullah, M. (2015). Exponentiated distributions. Paris: Atlantis Press.CrossRefGoogle Scholar
Bagdonavicius, V. & Nikulin, M. (2002). Accelerated life models: Modeling and statistical analysis. Boca Raton: Chapman and Hall, CRC.Google Scholar
Balakrishnan, N., Haidari, A., & Masoumifard, K. (2015). Stochastic comparisons of series and parallel systems with generalized exponential components. IEEE Transactions on Reliability 64: 333–348.CrossRefGoogle Scholar
Balakrishnan, N. & Rao, C.R. (1998). Order statistics: Theory and methods. In Handbook of statistics, vol. 16. New York: Elsevier.Google Scholar
Balakrishnan, N. & Rao, C.R. (1998). Order statistics: Applications. In Handbook of statistics, vol. 17. New York: Elsevier.Google Scholar
Balakrishnan, N. & Zhao, P. (2013). Ordering properties of order statistics from heterogeneous populations: A review with an emphasis on some recent developments. Probability in the Engineering and Informational Sciences 27: 403–443.CrossRefGoogle Scholar
Barlow, R.E. & Proschan, F. (1981). Statistical theory of reliability and life testing: Probability models. Silver Spring, MD: To Begin With.Google Scholar
Barmalzan, G., Payandeh Najafabadi, A.T., & Balakrishnan, N. (2019). Ordering results for series and parallel systems comprising heterogeneous exponentiated Weibull components. Communications in Statistics - Theory and Methods 48: 660–675.CrossRefGoogle Scholar
Cheng, K.W. (1977). Majorization: Its extensions and preservation theorems. Tech. Rep. No. 121. Department of Statistics, Stanford University, Stanford, CA.Google Scholar
Cordeiro, G.M., Ortega, E.M.M., & Silva, G.O. (2009). The exponentiated generalized gamma distribution with application to lifetime data. Journal of Statistical Computation and Simulation 81: 827–842.CrossRefGoogle Scholar
David, H.A. & Nagaraja, H.N. (2003). Order statistics, 3rd ed. Hoboken, NJ: John Wiley & Sons.CrossRefGoogle Scholar
Ding, W., Yang, J., & Ling, X. (2017). On the skewness of extreme order statistics from heterogeneous samples. Communications in Statistics - Theory and Methods 46: 2315–2331.CrossRefGoogle Scholar
Fang, L. & Xu, T. (2019). Ordering results of the smallest and largest order statistics from independent heterogeneous exponentiated gamma random variables. Statistica Neerlandica 73: 197–210.CrossRefGoogle Scholar
Fang, L. & Zhang, X. (2015). Stochastic comparisons of parallel systems with exponentiated Weibull components. Statistics & Probability Letters 97: 25–31.CrossRefGoogle Scholar
Haidari, A. & Payandeh Najafabadi, A.T. (2019). Characterization ordering results for largest order statistics from heterogeneous and homogeneous exponentiated generalized gamma variables. Probability in the Engineering and Informational Sciences 33: 460–470.CrossRefGoogle Scholar
Haidari, A., Payandeh Najafabadi, A.T., & Balakrishnan, N. (2019). Comparisons between parallel systems with exponentiated generalized gamma components. Communications in Statistics - Theory and Methods 48: 1316–1322.CrossRefGoogle Scholar
Haidari, A., Payandeh Najafabadi, A.T., & Balakrishnan, N. (2020). Application of weighted and unordered majorization orders in comparisons of parallel systems with exponentiated generalized gamma components. Brazilian Journal of Probability and Statistics 34: 150–166.CrossRefGoogle Scholar
Khaledi, B.E., Farsinezhad, S., & Kochar, S.C. (2011). Stochastic comparisons of order statistics in the scale model. Journal of Statistical Planning and Inference 141: 276–286.CrossRefGoogle Scholar
Kleiber, C. & Kotz, S. (2003). Statistical size distributions in economics and actuarial sciences. New York: John Wiley & Sons.CrossRefGoogle Scholar
Kundu, A. & Chowdhury, S. (2016). Ordering properties of order statistics from heterogeneous exponentiated Weibull models. Statistics & Probability Letters 114: 119–127.CrossRefGoogle Scholar
Kundu, A., Chowdhury, S., Nanda, A.K., & Hazra, N.K. (2016). Some results on majorization and their applications. Journal of Computational and Applied Mathematics 301: 161–177.CrossRefGoogle Scholar
Lai, C.D. & Xie, M. (2006). Stochastic ageing and dependence for reliability. New York: Springer.Google Scholar
Lu, L., Wu, Q., & Mao, T. (2020). Stochastic comparisons of largest-order statistics for proportional reversed hazard rate model and applications. Journal of Applied Probability 57: 832–852.Google Scholar
Mitrinović, D.S., Pečarić, J.E., & Fink, A.M. (1993). New inequalities in analysis. Dordrecht: Kluwer Academic Publishers.Google Scholar
Nadarajah, S. & Haghighi, F. (2011). An extension of the exponential distribution. Statistics 45: 543–558.CrossRefGoogle Scholar
Nikulin, M. & Haghighi, F. (2006). A chi-squared test for the generalized power Weibull family for the head-and-neck cancer censored data. Journal of Mathematical Sciences 133: 1333–1341.CrossRefGoogle Scholar
Shaked, M. & Shanthikumar, J.G. (2007). Stochastic orders. New York: Springer.CrossRefGoogle Scholar
Wang, J. (2018). Likelihood ratio ordering of parallel systems with heterogeneous scaled components. Probability in the Engineering and Informational Sciences 32: 460–468.CrossRefGoogle Scholar
Wang, J. & Cheng, B. (2017). Answer to an open problem on mean residual life ordering of parallel systems under multiple-outlier exponential models. Statistics & Probability Letters 130: 80–84.CrossRefGoogle Scholar
Wang, J. & Cheng, B. (2021). On likelihood ratio ordering of parallel systems with heterogeneous exponential components. Statistics & Probability Letters 175: 109118.CrossRefGoogle Scholar
Zhang, Y., Cai, X., Zhao, P. & Wang, H. (2018). Stochastic comparisons of parallel and series systems with heterogeneous resilience-scaled components. Statistics: A Journal of Theoretical and Applied Statistics 53: 126–147.CrossRefGoogle Scholar
Zhao, P. & Balakrishnan, N. (2009). Mean residual life order of convolutions of heterogeneous exponential random variables. Journal of Multivariate Analysis 100: 1792–1801.CrossRefGoogle Scholar
Zhao, P. & Balakrishnan, N. (2011). MRL ordering of parallel systems with two heterogeneous components. Journal of Statistical Planning and Inference 141: 631–638.CrossRefGoogle Scholar