Convergence of distributions of extremal independent random variables
The results of two previous papers of the author [Litov. Mat. Sb. 27, No.2, 219-223 (1987; Zbl 0636.62009), ibid. 28, No.2, 211-214 (1988; Zbl 0647.62031)] are extended here to the case of triangular arrays of independent random variables \(\{X_{nj},\quad 1\leq j\leq k_ n,\quad n\geq 1\}.\) Namely, the author finds nonuniform estimations of the speed of convergence of distribution functions of the maxima \(Z(n)=\max \{X_{nj}:\;1\leq j\leq k_ n\}\) and \(Z(N_ n)=\quad \max \{X_{nj}:\;1\leq j\leq N_ n\},\) where \(\{N_ n\}\) is a sequence of random indices independent of \(\{X_{nj}\}\).
triangular arrays of independent random variables
scientific article; zbMATH DE number 4178223
scientific article