# zbMATH — the first resource for mathematics

On asymptotics of distribution of the ratio of sums of random variables. (Russian) Zbl 0719.62027
This paper deals with the limit distribution of the ratio $$\xi_ 1+...+\xi_ n/\eta_ 1+...+\eta_ n$$ where the couple $$(\xi_ j,\eta_ j)$$ consists of i.i.d. random variables. It also contains some applications of the obtained results to the asymptotic behaviour of $\int_{R^ n}[f(x_ 1)+...+f(x_ n)]/[g(x_ 1)+...+g(x_ n)]\mu (dx_ 1,...,dx_ n)$ where $$\mu$$ is a finite measure and f and g are $$\mu$$-integrable functions. Moreover the authors investigate the problem of statistical estimation of the parameter $$\alpha$$ of the distribution $F_{\alpha}(x)=1-\ell (x)x^{-\alpha}I(x>0),$ where $$\ell (x)$$ is a slowly varying function.

##### MSC:
 62E20 Asymptotic distribution theory in statistics 62F10 Point estimation 60F05 Central limit and other weak theorems
##### Keywords:
integrable functions; limit distribution