## On inverse moments of nonnegative random variables.(English)Zbl 0991.60003

The aim of this article is to investigate under which conditions the inverse moments of the form $$E[(1+X_n)^{-\alpha}]$$ can be approximated by the inverse of the moments, i.e. expressions of the form $$(1+EX_n)^{-\alpha}$$, for a sequence of nonnegative random variables $$(X_n)$$, and a real number $$\alpha >0$$. The authors provide (natural) sufficient conditions for which this is true, more precisely, that: $\lim_{n\to\infty} {E\bigl[ (1+X_n)^{-\alpha} \bigr] \over(1+EX_n)^{-\alpha}} =1.$

### MSC:

 6e+06 Probability distributions: general theory 6.2e+21 Asymptotic distribution theory in statistics
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### References:

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