Abstract
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.
Highlights
The standard statistical tests from the parametric domain play a vital role in decision-making problems and are popular in social sciences [1]
The paper extends the concept of the Jarque–Bera test from classical statistics to neutrosophic statistics
The classical JB test is limited to perform on exact values data
Summary
The standard statistical tests from the parametric domain play a vital role in decision-making problems and are popular in social sciences [1]. Neutrosophic Jarque–Bera test testing the null hypothesis that there is no significant difference between the data in hand and the normal distribution versus the alternative hypothesis that a significant difference exists. When the observations in the data are fuzzy, the existing JB test under classical statistics cannot be applied for testing the normality of the data. Motivating from the computational limitations of the existing JB test for the exact form data, we proposed a modified version of the present JB test for the fuzzy or interval-valued data. The proposed JB test is a generalized form of the existing JB test from classical statistics as it possesses the ability to deal with both exact and fuzzy forms data sets. The use of the developed JB test will be beneficial in situations where the observations under a problem are not certain, fuzzy, indeterminate, interval-valued, or in neutrosophic form
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