A Limit Theorem for Sums of Minima of Stochastic Variables
Grenander, Ulf
Ann. Math. Statist., Tome 36 (1965) no. 6, p. 1041-1042 / Harvested from Project Euclid
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We consider a sequence of independent and identically distributed positive stochastic variables $x_1, x_2, x_3, \cdots$ with the distribution function $F(x)$. Let $y_n$ be the smallest of the values taken by the $n$ first of these variables and $S_n = y_1 + y_2 + \cdots + y_n$. It is then shown that $S_n/\log n$ tends in probability to the value $F = \lim_{t\downarrow 0} t/F(t)$ assumed to exist as a finite or infinite number.
Publié le : 1965-06-14
Classification:  
@article{1177700076,
     author = {Grenander, Ulf},
     title = {A Limit Theorem for Sums of Minima of Stochastic Variables},
     journal = {Ann. Math. Statist.},
     volume = {36},
     number = {6},
     year = {1965},
     pages = { 1041-1042},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177700076}
}

Grenander, Ulf. A Limit Theorem for Sums of Minima of Stochastic Variables. Ann. Math. Statist., Tome 36 (1965) no. 6, pp.  1041-1042. http://gdmltest.u-ga.fr/item/1177700076/