Normality Testing under Neutrosophic Statistics

Abstract

The normal distribution has been extensively been used in the statistical inference and decision
making problems. One of the main assumptions of the existing tests in classical statistics is that the
data should be from normally distributed population.Shapiro- Wilk test is widely used to test the
normality of data when the observations are precise or exact in nature. But in many areas including
agriculture, engineering and reliability, the data may be in interval form, indeterminate form or
uncertain. In such cases, the existed Classical Shapiro- Wilk test fails to test the normality of data.
In this paper, we proposed the Shapiro- Wilk test under neutrosophic environment to check whether
the uncertain data is from neutrosophic normal distribution or not. The hypothesis testing process
is executed on the observations based on lifetime of batteries. The comparative analysis has been
done with the existed Shapiro- Wilk test.The comparison shows that the proposed test is efficacious,
appropriate and well-suited to be applied in scenarios involving indeterminacy.