Neutrosophic Credibility Bounds for the ZB Distribution: Theory, Simulation, and Applications

Abstract

This paper introduces the ZB distribution, a novel mixture model that combines the exponential and Gamma distributions to flexibly capture both light- and heavy-tailed behaviours in uncertain data. Analytical expressions for the probability density function, cumulative distribution function, survival function, and hazard rate are derived in closed form.

To address hybrid uncertainty—stemming from both randomness and imprecision—the ZB distribution is integrated with neutrosophic logic and credibility theory. This integration leads to the formulation of Neutrosophic Credibility Bounds (NCBs), which provide interpretable interval estimates under varying degrees of truth, indeterminacy, and falsity.

A comprehensive simulation study explores how parameters such as the mixing proportion (θ) and credibility level (γ) influence the width and coverage of the bounds. Applications in insurance loss modeling, credit risk classification, and financial stress testing illustrate the practical utility of the proposed ZB–neutrosophic framework in data-driven decision-making