Some results on majorization and their applications

Ordering properties of sample minimum from Kumaraswamy-G random variables

“…So, if α ∈ D + i.e. if w ∈ E + and β ∈ E + (β ∈ D + ) then by Theorem 3.2 b)(i) (Theorem 3.1 b) (i)) of Kundu et al [14] it can be proved that r(β, x) is Schur convex on E + (Schur concave on D + ). This proves the result.…”

“…Thus by Theorem 3.1 b) (ii) of Kundu et al[14] and Lemma 2.1 the result is proved.2 Theorem 3.1 shows hr ordering between U 1:n and V 1:n when α majorizes γ keeping the other parameters same. Now the question arises-what will happen if β majorizes δ while the parameters α, γ are equal?…”

Stochastic Comparisons of Extreme Order Statistics in the Heterogeneous Exponentiated Scale Model

“…Note that by the assumptions xr(x) is convex in x. So, by Theorem 3.1 b(ii) (Theorem 3.2 a(ii)) of [21],r X n:n (x) is Schur convex. Thus, the result follows from Lemma 2.2.…”

Stochastic Comparisons of Parallel and Series Systems with Type II Half Logistic-Resilience Scale Components

“…In addition, there are some literature works that study the generalized exponential distribution, exponential Weibull distribution, and exponential generalized gamma distribution. The relevant research results can be found in the works of Balakrishnan [14], Fang and Zhang [15], Kundu et al [16], Kundu and Chowdhury [17], and Haidari et al [18], among others. Further, by introducing one or more parameters to a base distribution, the new distribution family has been favored by statisticians, for example adding a scale parameter λ to a base distribution F(x)(F(x)), which gives the scale distribution family F(λx)(F(λx)).…”