A Weibull-Based Critique of the Uniform Distribution in Interval Data Analysis

Abstract

In recent years, there has been a growing interest in neutrosophic probability distributions as effective tools for modeling data that involve uncertainty, ambiguity, or vagueness—limitations that classical probability models often fail to address. In addition, the simulation of interval data has been misapplied in neutrosophic analysis by assuming a uniform distribution over the interval. In this study, a neutrosophic extension of the Weibull distribution is used to generate neutrosophic data. From this data, the indeterminacy component, referred to as "indeterminacy factor," is extracted and estimated. To understand the behavior of this indeterminacy factor, several continuous probability distributions are fitted to its values. This paper makes three main contributions: (1) it presents a novel Neutrosophic Weibull distribution that can capture non-uniform indeterminacy patterns; (2) it offers a comparative analysis of several candidate distributions to assess the probabilistic framework of indeterminacy; and (3) it supports the suggested model using simulations and real-life data sets, proving its outstanding goodness-of-fit and practical importance. These findings emphasize the need for more suitable probabilistic models when dealing with neutrosophic data. Finally, the proposed neutrosophic Weibull distribution is applied to two real-world datasets containing uncertain observations. In both cases, the Weibull model shows the best fit. The corresponding indeterminacy values are then modeled using different probability distributions, and the results reflect similar patterns to those observed in the simulated neutrosophic data. Based on the analysis, it is concluded that the existing simulation—originally developed for interval analysis under a uniform distribution assumption—is not suitable for neutrosophic analysis.