Multivariate Analysis under Indeterminacy: An Application to Chemical Content Data.

Area of Science:

• Statistics
• Multivariate Analysis
• Uncertainty Quantification

Background:

• Classical Hotelling T-squared statistic is suitable for precise, exact multivariate data.
• Real-world data often involves uncertainty and imprecision due to complex measurements.
• Existing methods may be inadequate in uncertain environments.

Purpose of the Study:

• To introduce the Hotelling T-squared statistic within the framework of neutrosophic statistics (NS).
• To extend the applicability of Hotelling T-squared to uncertain data environments.
• To demonstrate the advantages of the neutrosophic Hotelling T-squared statistic.

Main Methods:

• Development of the Hotelling T-squared statistic under neutrosophic statistics.
• Application of the proposed statistic to real-world data exhibiting uncertainty.
• Comparative analysis with the classical Hotelling T-squared statistic.

Main Results:

• The neutrosophic Hotelling T-squared statistic is presented as a generalization of the classical approach.
• Demonstrated utility and benefits of the neutrosophic statistic through data analysis.
• Empirical evidence supports the effectiveness of the proposed method in uncertain conditions.

Conclusions:

• The neutrosophic Hotelling T-squared statistic is more adequate and effective for analyzing multivariate data under uncertainty.
• Neutrosophic statistics provides a robust framework for handling imprecision in statistical inference.
• The proposed method enhances the capability of Hotelling T-squared tests in complex, real-world scenarios.