A new goodness of fit test for normal distribution based on the negative cumulative extropy

In recent years, extropy has emerged as a compelling alternative measure of uncertainty in statistical analysis. This paper focuses on the negative cumulative residual extropy, as introduced by Tahmasebi and Toomaj [28], and leverages this concept to develop a novel goodness-of-fit test for normality. We rigorously examine the statistical properties of this new test statistic, including its mean and variance. Furthermore, we establish the percentiles of the test statistic’s distribution, allowing for practical implementation. To assess its effectiveness, we evaluate the power of the proposed test against a range of alternative distributions. Our simulation results reveal that the new test exhibits competitive power compared to existing methods. The test is computationally straightforward, and we demonstrate its practical application through the analysis of a real-world dataset.