Literal Neutrosophic and Plithogenic Marshall-Olkin Type II Class of Distributions with Application to Exponential Distribution

Danyah Dham¹, Mohamed Bisher Zeina², Riad K. Al-Hamido³

¹ Department of Mathematical Statistics, Faculty of Science, University of Aleppo, Syria.
² Department of Mathematical Statistics, Faculty of Science, University of Aleppo, Syria.
³ Department of Mathematical Statistics, Faculty of Science, Alfurat University, Syria

Emails: danyahdham@gmail.com; bisher.zeina@gmail.com; riad-hamido1983@hotmail.com.

Abstract

In this study, we introduce Marshall-Olkin type II class of distributions within the neutrosophic and plithogenic framework. We provide the formal expressions for the probability density function and derive the cumulative distribution function. As a specific instance, we examine the generalization of the exponential distribution in both neutrosophic and plithogenic forms according to this new class, presenting the probability density function and deriving the cumulative distribution function for this case. Furthermore, we propose an algorithm for generating random numbers based on this distribution. Additionally, we estimate its parameters using maximum likelihood and validate the results through a simulation study, demonstrating the efficiency of the calculated parameters. We also investigate the asymptotic properties, including unbiasedness and consistency.

Keywords: Marshall-Olkin Type II Class of Distributions; Neutrosophic; Plithogenic; AH Isometry; Maximum Likelihood Estimation; Random Numbers Generation.