On the Analysis of Variance Generalized Extropy Measure With Application to Engineering Data in Saudi Arabia

Measures of uncertainty such as entropy, extropy, varentropy, and varextropy play a fundamental role in statistical modeling and information analysis of probability distributions. In this article, we present and examine the variance of generalized extropy, providing a detailed investigation of its mathematical structure and theoretical characteristics. A comprehensive comparison with other information measures is carried out, with particular emphasis on ordered random variables. Additionally, the impact of monotonous transformations on the suggested measure is investigated, and several informative bounds are established. In addition, a novel stochastic order, referred to as the variance generalized extropy order, is proposed, and its main properties are discussed. The variance generalized extropy is further explored in the case of coherent systems and mixed system models. Finally, two nonparametric estimation procedures are developed and applied to two real datasets to demonstrate the practical usefulness of the proposed methodology.