A Tricentenary history of the Law of Large Numbers

  title={A Tricentenary history of the Law of Large Numbers},
  author={Eugene Seneta},
  • E. Seneta
  • Published 1 September 2013
  • Mathematics
  • Bernoulli
The Weak Law of Large Numbers is traced chronologically from its inception as Jacob Bernoulli's Theorem in 1713, through De Moivre's Theorem, to ultimate forms due to Uspensky and Khinchin in the 1930s, and beyond. Both aspects of Jacob Bernoulli's Theorem: 1. As limit theorem (sample size $n\to\infty$), and: 2. Determining sufficiently large sample size for specified precision, for known and also unknown p (the inversion problem), are studied, in frequentist and Bayesian settings. The Bienaym… 

On the Bicentenary in St. Petersburg of Jacob Bernoulli's Theorem

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The weak law of large numbers for nonnegative summands

  • E. Seneta
  • Mathematics
    Advances in Applied Probability
  • 2018
Abstract Khintchine's (necessary and sufficient) slowly varying function condition for the weak law of large numbers (WLLN) for the sum of n nonnegative, independent and identically distributed

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