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A distribution function F is a generalized distorted distribution of the distribution functions $$F_1,\ldots ,F_n$$ F 1 , … , F n if $$F=Q(F_1,\ldots ,F_n)$$ F = Q ( F 1 , … , F n ) for an increasing continuous distortion function Q such that $$Q(0,\ldots ,0)=0$$ Q ( 0 , … , 0 ) = 0 and $$Q(1,\ldots ,1)=1$$ Q ( 1 , … , 1 ) = 1 . In this paper, necessary...
We establish strong large deviation results for an arbitrary sequence of random vectors under some assumptions on the normalized cumulant generating function. In other words, we give asymptotic approximations for a multivariate tail probability of the same kind as the one obtained by Bahadur and Rao (Ann Math Stat 31:1015–1027, 1960) for the sample mean (in the one-dimensional case). The proof of...
In the paper, the Marcinkiewicz–Zygmund type moment inequality for extended negatively dependent (END, in short) random variables is established. Under some suitable conditions of uniform integrability, the $$L_r$$ L r convergence, weak law of large numbers and strong law of large numbers for usual normed sums and weighted sums of arrays of rowwise END random variables are investigated...
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