Article | REF: R250 V1

Estimators and hypothesis testing

Author: Jacques POIRIER

Publication date: July 10, 1992, Review date: August 18, 2022

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2. Specific laws used in estimates

2.1 Central limit theorem

Particularly important in practice, this theorem, which in reality admits several neighbouring, slightly different forms, legitimately allows a large number of distributions to be reduced to Gauss's law. We propose here to give various forms, without demonstration.

  • Let {X n }, n = 1,2,..., be a sequence of independent random variables with the same distribution, mean value m and standard deviation σ. The sequence {Y n }, n = 1,2,..., of random variables defined by :

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Specific laws used in estimates