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The weak law of large numbers for arrays
Statistics and Probability Letters, 1992Let \(\{X_{ni},1\leq i\leq k_ n,\;n\geq 1\}\), \(k_ n\to\infty\) as \(n\to\infty\), be an array of random variables and \[ {1\over k_ n}\sum^{k_ n}_{i=1}E| X_{ni}|^ pI\{| X_{ni}|>a\}\to 0\quad\text{as }a\to\infty ...
Allan Gut
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A remark on the Kolmogorov–Feller weak law of large numbers
Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2022Let \(X,X_{1},X_{2},...\) denote i.i.d. random variables and consider the partail sums \(S_{n}=X_{1}+X_{2}+...+X_{n}\). Also consider the mean \(\mu _{n}=EX1(\left\vert X\right\vert \leq n)\). The main result generalizes the Kolmogorov-Feller weak law of large numbers as follows.
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A Generalization of Weak Law of Large Numbers
Stochastic Analysis and Applications, 2011Kolmogorov's weak law of large numbers for i.i.d. random variables is generalized to a larger class distributions and to a wide class of normalizing sequences. The result is extended to maximal sums of negatively associated identically distributed random variables.
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On a Weak Law of Large Numbers with Regularly Varying Normalizing Sequences
Journal of Theoretical Probability, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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