Generating Neutrosophic Random Variables Based on

Generalized Gamma Distribution

Khalifa Al Shaqsi1,*

1 Department of Mathematical and Physical Sciences, College of Arts and Sciences, University of Nizwa, Oman

Received: September 10, 2025 Revised: November 03, 2025 Accepted: January 02, 2026 ⋆ Corresponding author

ABSTRACT

In practice, we encounter many systems that cannot be studied directly, either due to high costs or because some of

these systems are not directly detectable. Therefore, we resort to simulation, which involves applying the study to

systems similar to real-world systems and then projecting the results if they are suitable for the real system. The

simulation process requires a thorough understanding of probability distributions and the methods used to transform

random numbers following a regular distribution on [0,1] into random variables that follow it. This allows us to

maximize the benefits of the simulation process and obtain more accurate results for all emerging conditions. The

generalized gamma distribution is a family of three parameters characterized by high flexibility. It includes several

important distributions as special cases, including the gamma, Weibull, exponential, and Rayleigh distributions,

making it exceptionally valuable in engineering and reliability analysis. In previous research, we presented a

neutrosophic view of the process of generating random numbers and some techniques used to generate random

variables. In this research, we present a neutrosophic study for generating neutrosophic random variables following

the generalized gamma distribution, a distribution widely used in engineering applications. The neutrosophic

approach takes into account the uncertainty and indeterminacy of the parameters, resulting in random intervals for

the variables rather than specific values, and thus provides more accurate simulation results that adapt to all the

conditions that the system in operation may encounter.

Keywords: Simulation Random number generation Neutrosophic logic Generalized gamma distribution Neutrosophic

random variable generation Accept–reject technique

1. INTRODUCTION

Operations research is the applied branch of mathematics.

Since its inception, it has contributed to improving the performance

of many systems that utilize its methods in their

operations. Among the methods of operations research is

simulation. The importance of simulation in all branches of

science lies in the significant difficulty we may encounter

when studying the operation of any real-world system, either

due to high costs or the impossibility of studying some systems

directly. The simulation process relies on generating

a series of random numbers that follow a uniform probability

distribution in the range [0,1], and then transforming

these random numbers into random variables that follow the

probability distribution of the system being simulated.

Researchers interested in simulation have focused on providing

scientific methods that facilitate the transformation of

random numbers into random variables that follow probability

distributions more commonly used in practical applications.

To respond to the major advances brought about by neutrosophic

logic in all fields of science, many researchers have

presented studies aimed at offering a neutrosophic perspec-