The inverse moment for widely orthant dependent random variables

In this paper, we investigate approximations of the inverse moment model by widely orthant dependent (WOD) random variables. Let {Zn,n≥ 1} be a sequence of nonnegative WOD random variables, and {wni , 1≤ i≤ n,n≥ 1} be a triangular array of nonnegative nonrandom weights. If the first moment is finite, then E(a + ∑n i=1wniZi) –α ∼ (a +∑ni=1wniEZi)–α for all constants a > 0 and α > 0. If the rth moment (r > 2) is finite, then the convergence rate is presented as E(a+ ∑n i=1 wniZi) –α (a+ ∑n i=1 wniEZi) –α – 1 = O( 1 (a+ ∑n i=1 wniEZi ) 1–2β/r ), where β ≥ 0 and 2β/r < 1. Finally, some simulations illustrate the results. We generalize some corresponding results.