Using the Inverse Transformation Method to

Generate Random Variables that follow the Neutrosophic Uniform Probability Distribution

Maissam Jdid¹, A. Salama²

¹ Faculty of Informatics Engineering, Al-Sham Private University, Damascus, Syria

²  Department of Mathematics and Computer Science, Faculty of Science, Port Said University, Port Said, Egypt

  Emails: m.j.foit@aspu.edu.sy; drsalama44@gmail.com

Abstract

When conducting the simulation process for any of the systems  according to  classical logic, we  start by generating random numbers belonging to the regular probability distribution on the  field  [0, 1] using one of the known methods, and then we convert these random numbers into random variables  that follow the probability distribution that the system to be simulated works with,   the simulation process that we perform  it gives specific results that do not take into account the changes that may occur in the work environment of the system, to obtain more accurate results In a previous research, we prepared a study through which we reached random neutrosophic numbers follow the uniform distribution of the neutrosophic on  the field  with no determination that can be enjoyed by  the two parties  of the field, one or both together, it may be in the  form of a   group or a field   in another research  , we converted these neutrosophic random numbers into neutrosophic random variables that follow the neutrosophic exponential distribution using the opposite conversion method that depends on the cumulative distribution function of the probability distribution by which the  system to be simulated works, in this research  we have useda method  The opposite transformation to generate random variables that follow the neutrosophic uniform distribution and we have reached relationships through which  we can convert the neutrosophic random numbers that follow the   neutrosophic uniform distribution defined on the  domain   with the indeterminacy enjoyed by each end of the field, one or the other,  into  random variables that follow the neutrosophic uniform  distribution, which is a classical uniform distribution whose medians  are not precisely defined values , one or  both may be cognitiven in the form of a set or a domain, so  that n take into account all possible cases of mediators while maintaining the condition  ,  and the ;method was illustrated through an applied example and we came up with neutrosophic random variables that follow the uniform distribution that give us more accurate simulation results when used  due to the  indeterminacy of neutrosophic values.

Keywords: Uniform distribution; Simulation; Cumulative distribution function; Random numbers; Neutrosophic random variables