Neutrosophic Log-Logistic Distribution: a Novel Approach for Modeling Uncertain Survival and Reliability Data

Accepted - November 2024

Abstract

In survival and reliability engineering, log-logistic distribution is commonly employed, particularly for modeling lifetime data in electronic and human design processes. This research aims to present a modified neutrosophic log-logistic distribution (NLLD) designed to handle data indeterminacies. Unlike the approach by Rao (2023), which modeled the neutrosophic random variable as X_N∈
(X_L,X_U), our method defines it as X_N ∈ (1 + I_N)X_L. It is particularly useful for modeling ambiguous data with a roughly positive skew. This study examines the key statistical properties of the NLLD, including the neutrosophic mean, variance, median, quartiles, skewness, kurtosis, and reliability measures. Additionally, four modified entropy measures are derived for the NLLD, with numerical computations provided for the model. The maximum likelihood estimation method is used to estimate the neutrosophic parameters, and a simulation study is conducted to validate their accuracy. Finally, real-world applications demonstrate the effectiveness of the proposed NLLD compared to existing models.