Ordering results of the smallest order statistics from independent heterogeneous new modified generalized linear failure rate random variables

References

• Arnold, B. C., N. Balakrishnan, and H. N. Nagaraja. 1992. A first course in order statistics. New York: Wiley.
   Google Scholar
• Balakrishnan, N. 2007. Permanents, order statistics, outliers, and robustness. Revista Matematica Complutense 20 (1):7–107.
   Web of Science ®Google Scholar
• Balakrishnan, N., A. Haidari, and K. Masoumifard. 2015. Stochastic comparisons of series and parallel systems with generalized exponential components. IEEE Transactions on Reliability 64 (1):333–48. doi:10.1109/TR.2014.2354192.
   Web of Science ®Google Scholar
• Balakrishnan, N., P. Nanda, and S. Kayal. 2018. Ordering of series and parallel systems comprising heterogeneous generalized modified Weibull components. Applied Stochastic Models in Business and Industry 34 (6):816–34. doi:10.1002/asmb.2353.
   Web of Science ®Google Scholar
• Balakrishnan, N., and C. R. Rao. 1998. Order statistics: Applications. Handbook of statistics 17, 1st ed. Amsterdam; North-Holland: Elsevier.
   Google Scholar
• Balakrishnan, N., Y. Zhang, and P. Zhao. 2018. Ordering the largest claim amounts and ranges from two sets of heterogeneous portfolios. Scandinavian Actuarial Journal 2018 (1):23–41. doi:10.1080/03461238.2017.1278717.
   Web of Science ®Google Scholar
• Barmalzan, G., A. T. Payandeh Najafabadi, and N. Balakrishnan. 2019. Ordering results for series and parallel systems comprising heterogeneous exponentiated Weibull components. Communications in Statistics – Theory and Methods 48 (3):660–75. doi:10.1080/03610926.2017.1417433.
   Web of Science ®Google Scholar
• Bhattacharyya, D., R. A. Khan, and M. Mitra. 2020. Stochastic comparisons of series, parallel and k-out-of-n systems with heterogeneous bathtub failure rate type components. Physica A: Statistical Mechanics and Its Applications 540:123124. doi:10.1016/j.physa.2019.123124.
   Web of Science ®Google Scholar
• Chowdhury, S., and A. Kundu. 2017. Stochastic comparison of parallel systems with log-Lindley distributed components. Operations Research Letters 45 (3):199–205. doi:10.1016/j.orl.2017.02.005.
   Web of Science ®Google Scholar
• Das, S., and S. Kayal, and D. Choudhuri. 2021. Ordering results on extremes of exponentiated location-scale models. Probability in the Engineering and Informational Sciences 35 (2):331–54. doi:10.1017/S0269964819000408.
   Web of Science ®Google Scholar
• David, H. A., and H. K. Nagaraja. 2003. Order statistics. 3rd ed. Hoboken, NJ: John Wiley & Sons.
   Google Scholar
• Dykstra, R., S. C. Kochar, and J. Rojo. 1997. Stochastic comparisons of parallel systems of heterogeneous exponential components. Journal of Statistical Planning and Inference 65 (2):203–11. doi:10.1016/S0378-3758(97)00058-X.
   Web of Science ®Google Scholar
• Elbatal, I. 2013. Kumaraswamy generalized failure rate distribution. Indian Journal of Computational and Applied Mathematics 1 (1):61–78.
   Google Scholar
• Elbatal, I., F. Merovci, and W. Marzouk. 2014. MCDonald generalized linear failure rate distribution. Pakistan Journal of Statistics and Operation Research 10 (4):267–88. doi:10.18187/pjsor.v10i3.687.
   Google Scholar
• Fang, L., and N. Balakrishnan. 2017. Stochastic comparisons of series and parallel systems with generalized linear failure rate components. Applied Stochastic Models in Business and Industry 33 (2):248–55.
   Web of Science ®Google Scholar
• Fang, L., and N. Balakrishnan. 2018. Ordering properties of the smallest order statistics from generalized Birnbaum-Saunders models with associated random shocks. Metrika 81 (1):19–35. doi:10.1007/s00184-017-0632-1.
   Web of Science ®Google Scholar
• Fang, L., and X. Zhang. 2013. Stochastic comparisons of series systems with heterogeneous Weibull components. Statistics & Probability Letters 83 (7):1649–53. doi:10.1016/j.spl.2013.03.012.
   Web of Science ®Google Scholar
• Hazra, N. K., M. R. Kuiti, M. Finkelstein, and A. Nanda. 2017. On stochastic comparisons of maximum order statistics from the location - scale family of distributions. Journal of Multivariate Analysis 160:31–41. doi:10.1016/j.jmva.2017.06.001.
   Web of Science ®Google Scholar
• Jafari, A. A., and E. Mahmoudi. 2015. Beta-linear failure rate distribution and its applications. Journal of the Iranian Statistical Society 14 (1):89–105.
   Google Scholar
• Jamkhaneh, E. B. 2014. Modified generalized linear failure rate distribution; properties and reliability analysis. International Journal of Industrial Engineering Computations 5 (3):375–86.
   Google Scholar
• Khaledi, B. E., and S. C. Kochar. 2002. Dispersive ordering among linear combinations of uniform random variables. Journal of Statistical Planning and Inference 100 (1):13–21. doi:10.1016/S0378-3758(01)00091-X.
   Web of Science ®Google Scholar
• Khan, A. H., and T. R. Jan. 2016. The new modified generalized linear failure rate distribution. Journal of Statistics Applications & Probability Letters 3 (2):83–95. doi:10.18576/jsapl/030203.
   Google Scholar
• Kundu, A., and S. Chowdhury. 2016. Ordering properties of order statistics from heterogeneous exponentiated Weibull models. Statistics & Probability Letters 114:119–27. doi:10.1016/j.spl.2016.03.017.
   Web of Science ®Google Scholar
• Kundu, A., and S. Chowdhury. 2018. Ordering properties of sample minimum from Kumaraswamy-G random variables. Statistics 52 (1):133–46. doi:10.1080/02331888.2017.1353516.
   Web of Science ®Google Scholar
• Kundu, A., S. Chowdhury, A. Nanda, and N. Hazra. 2016. Some results on majorization and their applications. Journal of Computational and Applied Mathematics 301:161–77. doi:10.1016/j.cam.2016.01.015.
   Web of Science ®Google Scholar
• Li, C., and X. Li. 2015. Likelihood ratio order of sample minimum from heterogeneous Weibull random variables. Statistics & Probability Letters 97:46–53. doi:10.1016/j.spl.2014.10.019.
   Web of Science ®Google Scholar
• Mahmoud, M. A. W., and F. M. A. Alam. 2010. The generalized linear exponential distribution. Statistics & Probability Letters 80 (11-12):1005–14. doi:10.1016/j.spl.2010.02.015.
   Web of Science ®Google Scholar
• Marshall, A. W., I. Olkin, and B. C. Arnold. 2011. Inequalities: Theory of majorization and its applications. 2nd ed. New York: Springer.
   Google Scholar
• Patra, L. K., S. Kayal, and P. Nanda. 2018. Some stochastic comparisons results for series and parallel systems with heterogeneous Pareto type components. Applications of Mathematics 63 (1):55–77. doi:10.21136/AM.2018.0105-17.
   Web of Science ®Google Scholar
• Rinott, Y. 1973. Multivariate majorization and rearrangement inequalities with some applications to probability and statistics. Israel Journal Mathematics 15 (1):60–77. doi:10.1007/BF02771774.
   Google Scholar
• Shaked, M., and J. G. Shanthikumar. 2007. Stochastic orders. New York: Springer.
   Google Scholar
• Torrado, N., and S. C. Kochar. 2015. Stochastic order relations among parallel systems from Weibull distributions. Journal of Applied Probability 52 (1):102–16. doi:10.1239/jap/1429282609.
   Web of Science ®Google Scholar
• Wu, J., M. Wang, and X. Li. 2020. Convex transform order of the maximum of independent Weibull random variables. Statistics & Probability Letters 156:108597. doi:10.1016/j.spl.2019.108597.
   Web of Science ®Google Scholar
• Zhao, P., and N. Balakrishnan. 2011. Some characterization results for parallel systems with two heterogeneous exponential components. Statistics 45 (6):593–604. doi:10.1080/02331888.2010.485276.
   Web of Science ®Google Scholar