Neutrosophic Extension of the Transmuted Lindley
Distribution: Theory and Properties

Afrah Al Bossly^1,*

¹Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia

Email: a.basli@psau.edu.sa

Abstract

In this paper, we introduce a new extension of the transmuted Lindley distribution (TLD) by utilizing neutrosophic logic to handle uncertainties that are often found in real life data. As classical probability models are not flexible enough for dealing with vague, imprecise, ambiguous, and incomplete information, neutrosophic theory is more general as it handles indeterminacy part associated with data. The proposed neutrosophic transmuted Lindey distribution (NTLD) combines indeterminacy concept, yielding a powerful statistical distribution, which is suitable for modeling both randomness and indeterminacy. Major functions such as probability density function (PDF), cumulative function (CDF), reliability function (RF) and hazard rate function (HRF) are established in this framework. Graphical analysis and simulated data are used to illustrate the performance of the model. Moreover, important moments such as mean, variance, skewness, and kurtosis are computed for different values of the neutrosophic parameters. The proposed distribution provides a generalized approach to model complex and uncertain data in reliability engineering, survival analysis, and decision-making. A real electricity consumption data from energy sector is utilized to show the proposed model applicability.

Keywords: Neutrosophic logic; Lindley model; Neutrosophic probability; Estimation