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Statistical fractal analysis in testing the Hypotheses with imprecise data.
D Kalpanapriya1, N Shobana Devi1, M Mubashir Unnissa1
1Vellore Institute of Technology, India.
Methodsx
|December 16, 2024
Summary
This study introduces a novel statistical hypothesis testing method using fractal analysis and lacunarity for interval and fuzzy data. The new procedure provides decision rules and examples for hypothesis testing with uncertain data.
Area of Science:
- Statistics
- Fractal Analysis
- Data Science
Background:
- Traditional statistical methods often struggle with interval or fuzzy data.
- Fractal analysis offers new ways to characterize complex data structures.
- Lacunarity quantifies spatial heterogeneity in fractal patterns.
Purpose of the Study:
- Introduce a new statistical hypothesis testing procedure for interval population parameters.
- Incorporate fractal analysis and lacunarity into hypothesis testing.
- Extend the methodology to fuzzy data samples.
Main Methods:
- Developed a hypothesis testing framework using fractal dimensions.
- Integrated lacunarity to analyze the distribution of interval data.
- Defined decision rules for null and alternative hypotheses.
- Provided numerical examples for practical application.
- Extended the tests for fuzzy data sets.
Main Results:
- A novel statistical hypothesis testing procedure for real interval data was established.
- The method effectively utilizes lacunarity for parameter estimation.
- The procedure was successfully extended to handle fuzzy data hypotheses.
- Numerical examples demonstrated the practical applicability and robustness of the tests.
Conclusions:
- The proposed fractal analysis and lacunarity-based hypothesis testing offers a robust alternative for interval and fuzzy data.
- This approach enhances statistical analysis capabilities for complex and uncertain datasets.
- Further research can explore applications in various scientific domains requiring advanced statistical methods.
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