IMPLEMENTATION AND OPTIMIZATION OF PROBABILISTIC AND MATHEMATICAL STATISTICAL ALGORITHMS UNDER DISTRIBUTIVE ARCHITECTURE.

Statistical methods must be developed and optimized in distributed systems due to the increasing amount of data and processing demands in modern applications. The application and optimization of mathematical and probabilistic statistical methods in distributed computing settings is the main topic of this study. Algorithms like these have the potential to improve performance, scalability, and parallel processing abilities when integrated into distributed systems. We commence our investigation by reviewing current mathematical and probabilistic statistical algorithms, determining their advantages and disadvantages, and evaluating their suitability for distributed architectures. We then suggest new approaches for their smooth incorporation into distributed computing structures, making use of distributed storage and parallel processing to effectively manage massive datasets. Improving these algorithms' performance in distributed environments is the focus of this research's refinement phase. We seek to optimize the use of distributed infrastructures by minimizing latency and maximizing computational resources by investigating efficient communication protocols, load balancing mechanisms, and parallelization approaches. The suggested algorithms are put into practice inside a distributed structure for empirical confirmation, and their effectiveness is evaluated in comparison to more conventional, non-distributed competitors. We test the scaling, precision, and effectiveness of the methods in practical scenarios using a variety of datasets and use cases. [ABSTRACT FROM AUTHOR]