Generating Neutrosophic Random Variables Following the Poisson Distribution Using the Composition Method ( The Mixed Method of Inverse Transformation Method and Rejection Method)

Abstract

Simulation is a numerical technique used to perform tests on a numerical computer, and 
involves logical and mathematical relationships interacting with each other to describe the 
behavior and structure of a complex system in the real world over a period of time. Analysis 
using simulation is a "natural" and logical extension of the mathematical analytical models 
inherent in operations research, because most operations research methods depend on 
building mathematical models that closely approximate the real-world environment and we 
obtain the optimal solution for them using algorithms appropriate to the type of these models. 
The importance of the simulation process comes In all branches of science, there are many 
systems that cannot be studied directly, due to the great difficulty that we may encounter 
when studying, and the high cost, in addition to the fact that some systems cannot be studied 
directly. The simulation process depends on generating a series of numbers. Randomness 
subject to a uniform probability distribution over the domain [0,1] , then converting these 
numbers into random variables subject to the law of probability distribution by which the 
system to be simulated works, using known transformation methods. In previous research, 
we presented a neutrosophical vision of the reverse transformation method and the method 
of rejection and acceptance. Which are used to transform random numbers into random 
variables that follow probability distributions such as: uniform distribution, exponential 
distribution, beta distribution..., In this research, we present a neutrosophical vision of the 
Composition method )the mixed method of inverse transformation method and rejection 
method), used to generate random variables that follow... To some Poisson distribution, the 
aim is to obtain neutrosophic random variables that we use when simulating systems that 
operate according to this distribution in order to obtain more accurate simulation results. 

DOI: 10.5281/zenodo.10703089