Asymptotic Normality of Sums of Minima of Random Variables
Hoglund, Thomas
Ann. Math. Statist., Tome 43 (1972) no. 6, p. 351-353 / Harvested from Project Euclid
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Let $x_1, x_2,\cdots$ be independent and positive random variables with the common distribution function $F$. We show that if $\int^1_0|F(x) - x/b| \times x^{-2}dx < \infty$ for some $0 < b < \infty$, then $\sum^n_{k=1} \min(x_1,\cdots, x_k)$ is asymptotically normal with expectation $b \log n$ and variance $b^2 2 \log n$.
Publié le : 1972-02-14
Classification:  
@article{1177692730,
     author = {Hoglund, Thomas},
     title = {Asymptotic Normality of Sums of Minima of Random Variables},
     journal = {Ann. Math. Statist.},
     volume = {43},
     number = {6},
     year = {1972},
     pages = { 351-353},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177692730}
}

Hoglund, Thomas. Asymptotic Normality of Sums of Minima of Random Variables. Ann. Math. Statist., Tome 43 (1972) no. 6, pp.  351-353. http://gdmltest.u-ga.fr/item/1177692730/