LIMIT THEOREM FOR A STATISTIC PROPOSED BY V. HEFDLING
DOI:
https://doi.org/10.37547/Keywords:
Generalized statistics, sample size, normal distribution, independence, random variable, U-statistics, sequence of positive integer-valued random variables, distribution function, symmetry with respect to arguments.Abstract
The article first proves a limit theorem for a sequence of random variables called “U-statistics,” introduced by V. Hefdling. The proven limit theorem generalizes the result of V. Hefdling's theorem to the case where the number of samples is a random variable. In the theorem, it is not required that the observation results of the sample size are independent of the where ( ); however, as there must exist a sequence of numbers - with ( ) and a positive random variable such that, is required.
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