摘要
Let{X n}be a sequence of random variables and X n1X n2…X nn their order statistics.In this paper a central limit theorem and a strong law of large numbers for randomly trimmed sums T n=βn i=αn+1 X ni are established in the case thatαn andβn are positive integer-valued random variables such thatαn/n andβn/n converge to random variablesαandβrespectively with 0α<β1 in certain sense,and{X n}is aφ-mixing sequence.
Let{X n}be a sequence of random variables and X n1X n2…X nn their order statistics.In this paper a central limit theorem and a strong law of large numbers for randomly trimmed sums T n=βn i=αn+1 X ni are established in the case thatαn andβn are positive integer-valued random variables such thatαn/n andβn/n converge to random variablesαandβrespectively with 0α<β1 in certain sense,and{X n}is aφ-mixing sequence.
