Testing for seasonality using circular distributions based on non-negative trigonometric sums as alternative...

Area of Science:

• Epidemiology
• Biostatistics
• Statistical Modeling

Background:

• Detecting seasonal patterns in disease occurrence is vital for medical and epidemiological studies.
• Existing methods like the Edwards test and Cave and Freedman test have limitations in modeling complex seasonal patterns.
• Non-parametric tests such as Kuiper and Hewitt are also commonly used but may lack parametric flexibility.

Purpose of the Study:

• To develop a novel likelihood ratio test for seasonality.
• To utilize a flexible family of univariate circular distributions based on non-negative trigonometric sums (NNTS).
• To accommodate parametric alternative hypotheses with an arbitrary number of peaks and troughs.

Main Methods:

• Application of Fernández-Durán's family of NNTS distributions.
• Construction of a likelihood ratio test for seasonality.
• Comparison with existing parametric and non-parametric seasonality tests.

Main Results:

• The proposed test allows for parametric modeling of seasonality with multiple peaks and troughs.
• NNTS distributions provide a flexible framework for capturing complex seasonal disease patterns.
• The likelihood ratio test offers a robust approach to seasonality detection.

Conclusions:

• The developed likelihood ratio test provides a powerful tool for analyzing complex seasonal patterns in disease occurrence.
• This method enhances the ability to detect and understand seasonality in epidemiological data.
• The use of NNTS distributions offers a significant advancement in statistical modeling for seasonality.