Neutrosophic Credibility Bounds of the Xexponential Distribution

Abstract

Classical probability theory models uncertainty through precise distributions and point-based estimates. However, real-world data often exhibit imprecision, vagueness, and conflicting evidence—forms of uncertainty that traditional models are ill-equipped to handle. This paper proposes a novel framework for deriving credibility-based interval estimates for the Xexponential distribution using neutrosophic logic. Neutrosophic sets characterize uncertainty through independent measures of truth, indeterminacy, and falsity, providing a richer and more flexible representation. By integrating this with credibility theory, we define Neutrosophic Credibility Bounds (NCBs), which quantify the plausible range of a neutrosophic random variable governed by the Xexponential distribution. Analytical properties are derived, and a simulation study is conducted to explore the behavior of the bounds under varying credibility levels and thresholds.

The proposed model is also applied to real actuarial data, demonstrating its effectiveness in risk modeling where data incompleteness and subjectivity are prevalent. The framework offers a robust alternative to classical confidence intervals, particularly in decision-making environments shaped by hybrid uncertainty.