Simulation of Signed Probability Distributions

The notion of negative probability is almost one hundred years old, and so far, some results have been obtained in the direction of the theoretical development of the notion of extended probability. However, there is still a strong need for computational methods and tools, and the presented article is aimed at filling this gap. Several examples, including Feynman’s problem, of the numerical simulation of signed probability distributions are provided for the first time, along with the results of the simulation using the developed software toolbox. The presented methods and results might open wide possibilities for using signed probabilities in the fields of quantum computing, decision making, finance, insurance, large language models and artificial intelligence, and other fields where the use of signed probability distributions can extend the current level of mathematical modeling.