In this article, we compare extreme order statistics through vector majorization arising from heterogeneous Poisson and geometric random variables. These comparisons are carried out with respect to usual stochastic ordering.
ArnoldBCBalakrishnanN and NagarajaHN. A first course in order statistics. New York: Wiley, 1992.
2.
BarlowREProschanF.Statictical theory of reliability and life testing, probability models. New York: Holt Rinehart and Winston Inc., 1975.
3.
BalakrishnanNBarmalzanGand HaidariA. (2014). On usual multivariate stochastic ordering of order statistics from heterogeneous beta variables. Journal of Multivariate Analysis2014; 127: 147-150.
4.
ChenJZhangYZhaoP. (2019). Comparisons of order statistics from heterogeneous negative binomial variables with applications. Statistics: A Journal of Theoretical and Applied Statistics2019; 53(5): 1-22.
5.
ChowdhuryS and KunduA.Stochastic comparison of parallel systems with Log-Lindley distributed components. Operations Research Letters2017; 45(3): 199-205.
6.
ChowdhurySKunduA and MishraSK. On comparison of two parallel systems having Log-Lindley distributed components. Communications in Statistics - Theory and Methods2021. https//doi.org/10.1080/03610926.2021.1910838
7.
DaviesKDembiskaA. (2019). On the number of failed components in a k-out-of-n system upon system failure when the lifetimes are discretely distributed. Reliability Engineering & System Safety2019; 188: 47-61.
8.
DembiskaA.Discrete order statistics. In: Kotz S, Read C, Balakrishnan N, and Vidakovic B, editors, Encyclopedia of statistical sciences. Hoboken: Wiley; 2008.
9.
DykstraRKocharSCRojoJ.Stochastic comparisons of parallel systems of heterogeneous exponential components. Journal of Statistical Planning and Inference1997; 65: 203-211.
10.
FangL and ZhangX. Stochastic comparisons of parallel systems with exponentiated Weibull components. Statistics and Probability Letters2015; 97: 25-31.
11.
HazraNKKuitiMRFinkelsteinM and NandaAK. On stochastic comparisons of maximum order statistics from the location-scale family of distributions. Journal of Multivariate Analysis2017; 160: 31-41.
KhalediBEFarsinezhadS and KocharSC. Stochastic comparisons of order statistics in the scale model. Journal of Statistical Planning and Inference2011; 141; 276-286.
14.
KunduA and ChowdhuryS. Ordering properties of order statistics from heterogeneous exponentiated Weibull models. Statistics and Probability Letters2016; 114: 119-127.
15.
KunduA and ChowdhuryS.Ordering properties of sample minimum from Kumaraswamy-G random variables. Statistics: A Journal of Theoretical and Applied Statistics2018; 52(1): 133-146.
16.
KunduA and ChowdhuryS. On stochastic comparisons of series systems with heterogeneous dependent and independent location-scale family distributed components. Operations Research Letters2020; 48(1): 40-47.
17.
KunduA and ChowdhuryS. Ordering properties of the largest order statistics from Kumaraswamy-G models under random shocks. Communications in Statistics-Theory and Methods2021; 50(6): 1502-15141.
18.
KunduAChowdhuryS and BalakrishnanN. Ordering properties of the smallest and largest lifetimes in GompertzMakeham model. Communications in Statistics: Theory and Methods2021. https//doi.org/10.1080/03610926.2021.1919898.
19.
KunduAChowdhurySNandaAKHazraN. (2016). Some results on majorization and their applications. Journal of Computational and Applied Mathematics2016; 301: 161-177.
20.
LiX and FangR. Ordering properties of order statistics from random variables of Archimedean copulas with applications. Journal of Multivariate Analysis2015; 133: 304-320.
21.
LiCFangR and LiX. Stochastic comparisons of order statistics from scaled and interdependent random variables. Metrika2015; 79(5): 553-578.
22.
MarshallAWOlkinI and ArnoldBC. Inequalities: Theory of majorization and its applications. New York: Springer, 2011.
23.
MesouiMKayidM and IzadkhahS. Stochastic comparisons of order statistics from heterogeneous random variables with Archimedean copula. Metrika2017; 80(6): 749-766.
24.
NagarajaHN.Order statistics from discrete distributions. Statistics: A Journal of Theoretical and Applied Statistics1992; 23: 189-216.
25.
NavarroJ and SpizzichinoF.Comparisons of series and parallel systems with components sharing the same copula. Applied Stochastic Models in Business and Industry2010; 26(6): 775-791.
26.
ProschanF and SethuramanJ. Stochastic comparisons of order statistics from heterogeneous populations, with applications in reliability. Journal of Multivariate Analysis1976; 6(4): 608-616.
27.
RezapourM and AlamatsazMH. Stochastic comparison of lifetimes of two (n-k+1)-out-of-n systems with heterogeneous dependent components. Journal of Multivariate Analysis2014; 130: 240-251.
28.
ShakedM and ShanthikumarJG. Stochastic orders. New York: Springer; 2007.
29.
TorradoNandKocharSC.Stochastic order relations among parallel systems fromWeibull distributions. Journal of Applied Probability2015; 52: 102-116.
30.
XuM and HuT. Order statistics from heterogeneous negative binomial random variables. Probability in the Engineering and Informational Sciences2011; 25(4): 435.
31.
ZhaoP and BalakrishnanN. New results on comparison of parallel systems with heterogeneous gamma components. Statistics and Probability Letters2011; 81: 36-44.