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Abstract: We consider upper exponential bounds for the probability of the event that anabsolute deviation of sample mean from mathematical expectation p is biggercomparing with some ordered level epsilon. These bounds include 2 coefficients{alpha, beta}. In order to optimize the bound we are interested to minimizelinear coefficient alpha and to maximize exponential coefficient beta.Generally, the value of linear coefficient alpha may not be smaller than one.The following 2 settings were proved: 1 {1, 2} in the case of classicaldiscreet problem as it was formulated by Bernoulli in the 17th century, and 2{1, 2-1+epsilon^2} in the general discreet case with arbitrary rational p andepsilon. The second setting represents a new structure of the exponential boundwhich may be extended to continuous case.



Author: Vladimir Nikulin

Source: https://arxiv.org/



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