| Summary: | Abstract In this paper, we investigate approximations of the inverse moment model by widely orthant dependent (WOD) random variables. Let { Z n , n ≥ 1 } $\{Z_{n},n\geq1\}$ be a sequence of nonnegative WOD random variables, and { w n i , 1 ≤ i ≤ n , n ≥ 1 } $\{w_{ni},1\leq i\leq n,n\geq 1\}$ be a triangular array of nonnegative nonrandom weights. If the first moment is finite, then E ( a + ∑ i = 1 n w n i Z i ) − α ∼ ( a + ∑ i = 1 n w n i E Z i ) − α $E(a+ \sum_{i=1}^{n}w_{ni}Z_{i})^{-\alpha}\sim (a+\sum_{i=1}^{n}w_{ni}EZ_{i})^{-\alpha}$ for all constants a > 0 $a>0$ and α > 0 $\alpha>0$ . If the rth moment ( r > 2 $r>2$ ) is finite, then the convergence rate is presented as E ( a + ∑ i = 1 n w n i Z i ) − α ( a + ∑ i = 1 n w n i E Z i ) − α − 1 = O ( 1 ( a + ∑ i = 1 n w n i E Z i ) 1 − 2 β / r ) $\frac{E(a+\sum_{i=1}^{n}w_{ni}Z_{i})^{-\alpha}}{(a+\sum_{i=1}^{n}w_{ni}EZ_{i})^{-\alpha}}-1=O(\frac{1}{(a+\sum_{i=1}^{n}w_{ni}EZ_{i})^{1-2\beta/r}})$ , where β ≥ 0 $\beta\geq0$ and 2 β / r < 1 $2\beta/r<1$ . Finally, some simulations illustrate the results. We generalize some corresponding results.
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