The Basics of Neutrosophic Simulation for Converting Random Numbers Associated with a Uniform Probability Distribution into Random Variables Follow an Exponential Distribution

Abstract

When performing the simulation process, we encounter many systems that do not follow
by their nature the uniform distribution adopted in the process of generating the random numbers
necessary for the simulation process. Therefore, it was necessary to find a mechanism to convert the
random numbers that follow the regular distribution over the period [0, 1] to random variables that
follow the probability distribution that works on the system to be simulated. In classical logic, we
use many techniques in the transformation process that results in random variables that follow
irregular probability distributions. In this research, we used the inverse transformation technique,
which is one of the most widely used techniques, especially for the probability distributions for
which the inverse function of the cumulative distribution function can found. We applied this
technique to generate neutrosophic random variables that follow an exponential distribution or a
neutrosophic exponential distribution. This based on classical or neutrosophic random numbers that
follow a regular distribution. We distinguished three cases according to the logic that each of the
random numbers or the exponential distribution follows. We arrived at neutrosophic random
variables that, when we use them in systems that operate according to an exponential distribution,
such as queues and others, will provide us with a high degree of accuracy of results, and the reason
for this is due to the indeterminacy provided by neutrosophic logic