Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia.
College of Statistical and Actuarial Sciences, University of the Punjab Lahore, Lahore, Pakistan.
PLoS One. 2021 Dec 2;16(12):e0260689. doi: 10.1371/journal.pone.0260689. eCollection 2021.
In decision-making problems, the researchers' application of parametric tests is the first choice due to their wide applicability, reliability, and validity. The common parametric tests require the validation of the normality assumption even for large sample sizes in some cases. Jarque-Bera test is among one of the methods available in the literature used to serve the purpose. One of the Jarque-Bera test restrictions is the computational limitations available only for the data in exact form. The operational procedure of the test is helpless for the interval-valued data. The interval-valued data generally occurs in situations under fuzzy logic or indeterminate state of the outcome variable and is often called neutrosophic form. The present research modifies the existing statistic of the Jarque-Bera test for the interval-valued data. The modified design and operational procedure of the newly proposed Jarque-Bera test will be useful to assess the normality of a data set under the neutrosophic environment. The proposed neutrosophic Jarque-Bera test is applied and compared with its existing form with the help of a numerical example of real gold mines data generated under the fuzzy environment. The study's findings suggested that the proposed test is effective, informative, and suitable to be applied in indeterminacy compared to the existing Jarque-Bera test.
在决策问题中，由于参数检验具有广泛的适用性、可靠性和有效性，研究人员首先选择使用参数检验。即使在某些情况下样本量较大，常见的参数检验也需要验证正态性假设。Jarque-Bera 检验是文献中可用的方法之一，可用于达到此目的。Jarque-Bera 检验的限制之一是计算限制仅适用于精确形式的数据。该检验的操作程序对区间值数据无效。区间值数据通常出现在模糊逻辑或结果变量不确定状态下的情况中，通常称为 Neutrosophic 形式。本研究针对区间值数据修改了现有的 Jarque-Bera 检验统计量。新提出的 Jarque-Bera 检验的修改设计和操作程序将有助于在 Neutrosophic 环境下评估数据集的正态性。通过在模糊环境下生成的真实金矿数据的数值示例，应用并比较了所提出的 Neutrosophic Jarque-Bera 检验及其现有形式。研究结果表明，与现有的 Jarque-Bera 检验相比，所提出的检验在不确定性下更有效、信息更丰富、更适合应用。
