Journal of Jishou University(Natural Sciences Edition) ›› 2021, Vol. 42 ›› Issue (4): 4-8.DOI: 10.13438/j.cnki.jdzk.2021.04.002

• Mathematics • Previous Articles     Next Articles

Proof Converges with Probability That the k-th Order Central Absolute Moment of the Sample

XING Jiasheng, YANG Yichuan, WU Sang   

  1. (1. School of Mathematics, Beihang University, Beijing 100191, China; 2. LMIB of the Ministry of Education, Beihang University, Beijing 100191, China)
  • Online:2021-07-25 Published:2021-11-17

Abstract: Considering the problem of convergence in probability of the k-th order center absolute moment of the sample, using Khinchin’s law of large numbers and the property of convergence in probability of random variable sequences, through inequality scaling techniques, the concrete proof is given that the k-th order central absolute moment of the sample converges with probability to the k-th order central absolute moment of the population.

Key words: sample moment, population moment, center absolute moment, convergence in probability, inequality

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