On usual multivariate stochastic ordering of order statistics from heterogeneous beta variables

Ordering Results on Extremes of Exponentiated Location-Scale Models

“…Note that if all the location and shape parameters are known and set to zero and one, respectively, then the assumption made in Theorem 3.2(i) can be relaxed as shown in Theorem 3.2 of Khaledi et al [22]. (3,5,6), and (δ 1 , δ 2 , δ 3 ) = (2,4,9). All the conditions of Theorem 3.2(i) are satisfied.…”

“…Under certain conditions, they showed that the minimum order statistic of one set of random variables dominates that of other set of random variables with respect to various stochastic orders. We also refer to [3,16,17,39] for more results in this direction.…”

Comparisons of Order Statistics from Heterogeneous Poisson and Geometric Distributions

“…The concept of majorization order has been used for the last two decades in many diverse areas including management science, economics, physics, actuarial science, reliability theory and survival analysis. Comparison of smallest and largest order statistics from heterogeneous independent random variables following specific continuous distribution function can be found in Proschan and Sethuraman [26] , Dykstra et al [9] , Balakrishnan et al [3] , Fang and Zhang [10] , Zhao and Balakrishnan [31] , Torrado and Kochar [29] , Kundu et al [19] , Kundu and Chowdhury [141517] , Chowdhury and Kundu [56] and the references therein. One can find such comparisons under the same set-up for a family of continuous distributions in Khaledi et al [13] , Li et al [21] , Hazra et al [11] , and Kundu and Chowdhury.…”

Ordering properties of the largest order statistics from Kumaraswamy-G models under random shocks

“…, X n , then the sample minimum and sample maximum correspond to the smallest and the largest order statistics X 1:n and X n:n respectively. The results of stochastic comparisons of the order statistics (largely on the smallest and the largest order statistics) can be seen in Dykstra et al (1997), Fang and Balakrishnan (2018), Fang and Zhang (2015), Zhao and Balakrishnan (2011), Torrado and Kochar (2015), Balakrishnan et al (2014), Li and Li (2015), , Chowdhury (2016, 2018), Chowdhury and Kundu (2017) and the references there in for a variety of parametric models. The assumption in the papers lies in the fact that each of the order statistics X 1:n , X 2:n , .…”