Received 11.09.2024, Revised 05.12.2024, Accepted 31.12.2024

METHOD OF USING LAPLACE'S INTEGRAL THEOREM TO FIND THE PROBABILITY OF DIFFERENCE FROM THE CONSTANT PROBABILITY OF RELATIVE FREQUENCY IN INDEPENDENT TRIALS

B.A. Aalieva, A.T. Abdykerimova

Modern big-data tasks require methods for evaluating statistical deviations. This study pro- poses a method to estimate the probability of relative frequency deviation from a constant in inde- pendent trials. Using Laplace's theorem, this approach overcomes the large sample limitations of Bernoulli’s formula. The methodology analyzes the distribution asymptotic behavior and applies a Laplace function to calculate the boundary conditions. Experiments with a 400-element sample showed that, with an event probability of 0.1, a 0.03 deviation was achieved with 0.9544 proba- bility. Increasing data volume reduces estimated variance while maintaining prediction accuracy. 
This method enhances statistical modeling for quality control and risk analysis

statistical deviations, asymptotic behavior, Laplace function, boundary condi- tions, variance of estimates, prediction accuracy, independent trials, empirical indicators, computational resources, statistical modeling
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Aalieva, B.A., & Abdykerimova, A.T. (2024). METHOD OF USING LAPLACE'S INTEGRAL THEOREM TO FIND THE PROBABILITY OF DIFFERENCE FROM THE CONSTANT PROBABILITY OF RELATIVE FREQUENCY IN INDEPENDENT TRIALS. Bulletin of the Bishkek State University, 22(4), 3-8. https://doi.org/10.35254/bsu/2024.70.01

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