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The paper aims to derive local limit theorems for sequences of independent random variables using the saddlepoint method.

Local Limit Theorems for Large Deviations

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The paper aims to derive local limit theorems for sequences of independent random variables using the saddlepoint method.
Utilized saddlepoint method to analyze the distribution functions of independent random variables.
Derived relationships for distribution density under various conditions for large n.
Established new analytical limits for large deviations in the context of variable distributions.
Demonstrated that for large n, each Z_n possesses an analytical distribution density.
Showed the relationship between p_{z_n}(x) and normal distribution density, with precise mathematical formulation.
Provided weakened conditions for the limit theorem for identically distributed random variables.

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Randomized trial explores local limit theorems for large deviations in random variables, indicating new insights into distribution densities.

W. Richter (1957) studied this question.

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Randomized trial explores local limit theorems for large deviations in random variables, indicating new insights into distribution densities.