References
- Pledger P, Proschan F, Comparisons of order statistics and of spacings from heterogeneous distribution. In: Rustagi JS, editor. Optimizing methods in statistics. New York: Academic Press; 1971. p. 89–113.
- Dykstra R, Kochar SC, Rojo J. Stochastic comparisons of parallel systems of heterogeneous exponential components. J Stat Plan Inference. 1997;65:203–211. doi: 10.1016/S0378-3758(97)00058-X
- Khaledi BE, Kochar SC. Some new results on stochastic comparisons of parallel systems. J Appl Probab. 2000;37:1123–1128. doi: 10.1239/jap/1014843091
- Joo S, Mi J. Some properties of hazard rate functions of systems with two components. J Stat Plan Inference. 2010;140:444–453. doi: 10.1016/j.jspi.2009.07.023
- Zhao P, Balakrishnan N. Some characterization results for parallel systems with two heterogeneous exponential components. Statistics. 2011;45:593–604. doi: 10.1080/02331888.2010.485276
- Khaledi BE, Kochar SC. Weibull distribution: some stochastic comparisons results. J Stat Plan Inference. 2006;136:3121–3129. doi: 10.1016/j.jspi.2004.12.013
- Kochar SC, Xu M. Stochastic comparisons of parallel systems when components have proportional hazard rates. Probab Eng Inform Sci. 2007;21:597–609. doi: 10.1017/S0269964807000344
- Fang L, Zhang X. Stochastic comparisons of series systems with heterogeneous Weibull components. Stat Probab Lett. 2013;83:1649–1653. doi: 10.1016/j.spl.2013.03.012
- Torrado N. Comparisons of smallest order statistics from Weibull distributions with different scale and shape parameters. J Korean Stat Soc. 2015;44:68–76. doi: 10.1016/j.jkss.2014.05.004
- Torrado N, Kochar SC. Stochastic order relations among parallel systems from Weibull distributions. J Appl Probab. 2015;52:102–116. doi: 10.1239/jap/1429282609
- Zhao P, Balakrishnan N. New results on comparisons of parallel systems with heterogeneous gamma components. Stat Probab Lett. 2011;81:36–44. doi: 10.1016/j.spl.2010.09.016
- Balakrishnan N, Zhao P. Hazard rate comparison of parallel systems with heterogeneous gamma components. J Multivar Anal. 2013;113:153–160. doi: 10.1016/j.jmva.2011.05.001
- Zhao P, Zhang Y. On the maxima of heterogeneous gamma variables with different shape and scale parameters. Metrika. 2014;77:811–836. doi: 10.1007/s00184-013-0466-4
- Zhang Y, Zhao P. On the maxima of heterogeneous gamma variables. Commun Stat Theory Methods. 2017;46:5056–5071. doi: 10.1080/03610926.2015.1091084
- Fang L, Zhang X. Stochastic comparisons of parallel systems with exponentiated Weibull components. Stat Probab Lett. 2015;97:25–31. doi: 10.1016/j.spl.2014.10.017
- Balakrishnan N, Haidari A, Masoumifard K. Stochastic comparisons of series and parallel systems with generalized exponential components. IEEE Trans Reliab. 2015;64:333–348. doi: 10.1109/TR.2014.2354192
- Kundu A, Chowdhury S. Ordering properties of order statistics from heterogeneous exponentiated Weibull models. Stat Probab Lett. 2016;114:119–127. doi: 10.1016/j.spl.2016.03.017
- Kundu A, Chowdhury S, Nanda AK, et al. Some results on majorization and their applications. J Comput Appl Math. 2016;301:161–177. doi: 10.1016/j.cam.2016.01.015
- Khaledi BE, Farsinezhad S, Kochar SC. Stochastic comparisons of order statistics in the scale model. J Stat Plan Inference. 2011;141:276–286. doi: 10.1016/j.jspi.2010.06.006
- Kochar SC, Torrado N. On stochastic comparisons of largest order statistics in the scale model. Commun Stat Theory Methods. 2015;44:4132–4143. doi: 10.1080/03610926.2014.985839
- Misra N, Misra AK. New results on stochastic comparisons of two-component series and parallel systems. Stat Probab Lett. 2012;82:283–290. doi: 10.1016/j.spl.2011.10.010
- Ding W, Zhang Y, Zhao P. Comparisons of k-out-of-n systems with heterogenous components. Stat Probab Lett. 2013;83:493–502. doi: 10.1016/j.spl.2012.10.012
- Hazra NK, Kuiti MR, Finkelstein M, et al. On stochastic comparisons of maximum order statistics from the location-scale family of distributions. J Multivar Anal. 2017;160:31–41. doi: 10.1016/j.jmva.2017.06.001
- Hazra NK, Kuiti MR, Finkelstein M, et al. On stochastic comparisons of minimum order statistics from the location-scale family of distributions. Metrika. 2018;81:105–123. doi: 10.1007/s00184-017-0636-x
- Li X, Fang R. Ordering properties of order statistics from random variables of Archimedean copulas with applications. J Multivar Anal. 2015;133:304–320. doi: 10.1016/j.jmva.2014.09.016
- Li C, Fang R, Li X. Stochastic comparisons of order statistics from scaled and interdependent random variables. Metrika. 2016;79:553–578. doi: 10.1007/s00184-015-0567-3
- Fang R, Li C, Li X. Stochastic comparisons on sample extremes of dependent and heterogenous observations. Statistics. 2016;50:930–955. doi: 10.1080/02331888.2015.1119151
- Mudholkar GS, Srivastava DK. Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Trans Reliab. 1993;42:299–302. doi: 10.1109/24.229504
- Müller A, Stoyan D. Comparison methods for stochastic models and risks. New York: John Wiley & Sons; 2002.
- Shaked M, Shanthikumar JG. Stochastic orders. New York: Springer-Verlag; 2007.
- Marshall AW, Olkin I, Arnold BC. Inequalities: theory of majorization and its applications. 2nd ed. New York: Springer-Verlag; 2011.
- Nelsen RB. An introduction to copulas. Springer: New York; 2006.
- McNeil AJ, Něslehová J. Multivariate Archimedean copulas, D-monotone functions and l1-norm symmetric distributions. Ann Stat. 2009;37:3059–3097. doi: 10.1214/07-AOS556
- Fang R, Li C, Li X. Ordering results on extremes of scaled random variables with dependence and proportional hazards. Statistics. 2018;52:458–478. doi: 10.1080/02331888.2018.1425998
- Marshall AW, Olkin I. Life distributions. New York: Springer; 2007.
- Ding W, Yang J, Ling X. On the skewness of extreme order statistics from heterogenous samples. Commun Stat Theory Methods. 2017;46:2315–2331. doi: 10.1080/03610926.2015.1041984
- Ahmed AN, Alzaid A, Bartoszewicz J, et al. Dispersive and superadditive ordering. Adv Appl Probab. 1986;18:1019–1022. doi: 10.2307/1427262
- Belzunce F, Candel J, Ruiz JM. Ordering and asymptotic properties of residual income distributions. Sankhyā. 1998;60:331–348.
- Misra N, Francis J, Naqvi S. Some sufficient conditions for relative aging of life distributions. Probab Eng Inform Sci. 2017;31:83–99. doi: 10.1017/S0269964816000309
- Saunders IW, Moran PA. On the quantiles of the gamma and F distributions. J Appl Probab. 1978;15:426–432. doi: 10.2307/3213414