The Neutrosophic New XLindley Distribution: Statistical  Properties, Estimation, Simulation, and Application

Fatima Zohra Zeghbib; Halim Zeghdoudi

Authors

Fatima Zohra Zeghbib Department of Mathematics, Laboratory of LAMAHIS, University of 20 Aoˆut 1955, El-Hedaiek, Skikda, Algeria;
Halim Zeghdoudi LaPS Laboratory, Badji Mokhtar-Annaba University, Box 12, Annaba 23000, Algeria;

Keywords:

neutrosophic statistics; X-Lindley distribution; credibility bounds; maximum likelihood; Bayesian estimation; simulation study; insurance modeling

Abstract

This paper introduces a novel framework for deriving neutrosophic credibility bounds within the
context of the Neutrosophic New X-Lindley Distribution (NNXLD), an extension of the classical X-Lindley dis
tribution that integrates indeterminate and imprecise information. The main focus is to construct neutrosophic
Bayes estimators and contrast their performance with classical Bayesian estimators, highlighting the enhanced
f
lexibility offered in modeling uncertainty. The methodology includes the derivation of statistical properties of
the NNXLD and the implementation of three estimation techniques—Maximum Likelihood Estimation (MLE),
Method of Moments (MoM), and Bayesian estimation under a Gamma prior. A simulation study evaluates
the estimators’ accuracy using bias, mean squared error, and standard deviation across varying sample sizes.
Furthermore, the model’s real-world relevance is illustrated through an application to insurance claim severity
data, demonstrating its robust fit in the presence of uncertainty. The results confirm the practical advantages
of neutrosophic modeling in handling vague, incomplete, or subjective data, making the NNXLD a valuable
tool in reliability and actuarial science.

DOI 10.5281/zenodo.17216367